The small museum in County Kildare is putting on the exhibition in part because its owner knows Cobain's family.
Kurt Cobain's daughter has said the United States needs to overcome its taboo about mental health and addiction almost a quarter of century after her rock star father took his own life.
Frances Bean Cobain was speaking on Tuesday in Ireland at the launch of a new exhibition of the Nirvana frontman's belongings. Cobain died in 1994 aged 27 from a self-inflicted gunshot while struggling with heroin addiction.
"There is an association that is shameful and it shouldn't be," Frances Bean said, who has also struggled with addiction.
"It's taboo ... despite the fact that it is present in our society every single day. And I think that in Europe it is a little less taboo, I think in America it is very, very frowned upon," she told said.
Frances Bean, Cobain's sister Kim, and mother, Wendy O'Connor, attended the opening of the exhibition at the Museum of Style Icons in Newbridge, 50 km southwest of Dublin.
From his sketches and drawings to clothing and a car, "Growing Up Kurt Cobain" displays dozens of Cobain's personal items, some of them never seen before by the public.
Fans of Cobain, who popularized grunge rock in the early 1990s, can see the striped green sweater he wore in the video for Nirvana's 1991 hit "Smells Like Teen Spirit" and his MTV Video award for the same song.
The singer's childhood drawings of cartoon characters, handwritten lyrics and powder-blue 1965 Dodge Dart car are also on display.
The small museum in County Kildare is holding the exhibition in part because its owner knows Cobain's family. The museum also has outfits worn by the likes of Audrey Hepburn, Elizabeth Taylor and Grace Kelly on display, and has previously hosted exhibitions dedicated to Michael Jackson and Prince.