Chimamanda Ngozi Adichie, the best-selling Nigerian author, wants American readers to know that African writers don’t just write about Africa’s problems. “When we talk about the developing world, there’s this idea that everybody should be fighting for the poor,” she says. Though it might seem obvious to point out, she adds, “people are diverse, and there are different things that are going on with them.”

She calls it the “danger of a single story”—the idea that people living in certain areas of the world all have one kind of experience. Ms. Adichie hopes to show audiences Africa’s range of stories as the co-curator of this year’s PEN World Voices Festival. For the first time, the weeklong literature event, which starts Monday in New York, will have a regional focus. Along with other book-related programs, authors from Africa and its diaspora will speak about topics like how the West misunderstands African culture and the state of Africa’s poetry scene.

Ms. Adichie, 37, has spent her adult life traveling between the U.S. and Nigeria. She first rose to prominence in 2003 with the publication of her first book, “Purple Hibiscus,” a coming-of-age novel set in postcolonial Nigeria. She went on to write two more critically-acclaimed novels, “Half of a Yellow Sun” (2006) and “Americanah” (2013), as well as a collection of short stories. She won a MacArthur “genius” grant in 2008.

Ms. Adichie hopes that the spotlight of the PEN festival will help to win a wider audience for the African writers she’s chosen, including Nigerian-American author Teju Cole and Cameroonian writer Achille Mbembe. “It was important to get people who actually live on the continent,” along with those who have left, said Ms. Adichie by phone from her part-time residence in Columbia, Md. “I think the voices of the African diaspora are important too, but I think there’s often a silence in our voices from the continent.”

Ms. Adichie spent much of her childhood in the town of Nsukka at the University of Nigeria, where her father was a professor and her mother was an administrator. She describes the campus as a closed community, where she attended elementary school and a secondary school on the premises, and stayed for part of college.

Then Ms. Adichie decided she wanted to study in the U.S. instead. She arrived in 1998, and her first shock was finding poverty. Growing up, she had watched many American movies and TV shows, and the conditions that she saw driving through Philadelphia on her way to Drexel University jarred her. Another surprise was her roommate’s pity when Ms. Adichie told her that she had grown up in Africa.

She found that she enjoyed the freedom of the American higher education system. In Nigeria, she says, students were encouraged to focus on one discipline. “One of the things that I loved about the U.S. is that the walls could be broken down,” she says. “You could take philosophy, history and biology, and that wouldn’t happen in Nigeria.” She transferred from Drexel to Eastern Connecticut State University, where she studied communications and political science, while writing on the side. She later earned master’s degrees from Johns Hopkins University and Yale. Then she started writing full-time.

Ms. Adichie says that she felt different from other writers in at least one way: Many of them were able to draw dramatic tales from their difficult early family lives, but her upbringing had been happy. “I feel a little bit guilty for not having massive trauma in my childhood,” she says.

She does, however, experience bouts of depression, “the crazy writer illness” that she thinks is common in her field. “There’s something comforting about that, because you feel you’re not alone,” she says.

Her books have some parallels to her own experience. In “Americanah,” the female protagonist leaves Nigeria to go to college in the U.S., where she faces culture shock. It won a National Book Critics Circle Award and last year, Brad Pitt announced that he would produce a film version, starring Lupita Nyong’o.

She has mixed feelings about both Nigeria and the U.S., where her husband works as a doctor in Baltimore. “I love Nigeria, but it’s a very clear-eyed love,” she says. “I know Nigeria has a lot of problems, but I also know that Nigeria is not about its problems.” She has written about electricity outages in Lagos, for one, and thinks that the privatization of energy companies should have improved service more. The country’s elections in March made Ms. Adichie more optimistic about Nigeria’s prospects. “It was proof that democracy…is making progress,” she says.

In the U.S., she says, she has always felt more like a visitor. (She continues to be a Nigerian citizen.) American grocery stores distress her because so many of the foods on offer are unhealthy. “Why do American supermarkets need so much sugar in everything?” she asks. “If you’re this wealthy, something can be done so vegetables are cheap.”

As for broader issues, she says that “race is a present thing in America, and it isn’t in Nigeria.” But gender is a problem in her homeland. She recounts how, when she recently walked into a grocery store with her brother there, the security guard at the entrance only greeted him. “I was not in a good mood, so I said, ‘This has to change. You have to greet the both of us.’” The difficulty, she says, is that “the invisibility of the female” is part of Nigerian culture.

At the TED conference in 2013, Ms. Adichie gave a now-famous talk titled, “We Should All Be Feminists.” (The singer Beyoncé quoted it in her song “Flawless.”) “My version of feminism means acknowledging that women have and continue to have gotten the bad end of things, politically and socially, all over the world,” she says. “Feminism means not only acknowledging that, but wanting to make it better.”

Known for dressing in bright, bold prints, Ms. Adichie says that her mother influenced her preference for lively attire. Also, “Nigerians are just really interested in appearance, and it cuts across class,” she says. “Lagos is the most stylish city in the world.” Ms. Adichie has most of her clothing custom-made and says that she has a notion “in my delusion” of designing her own clothing.

Meanwhile, some days she writes for 12 hours straight; other days she can’t bring herself to write at all.

“I wish I could write every day, but I don’t,” she says. “When it goes well, I ignore things like family and hygiene, but other days, when it’s not going well, I read the books I love to remind myself of how beautiful and essential and nurturing words can be, and I hope that doing that will bring my own words back.”