The Hole singer said she contacted Los Angeles authorities about the identity scam last week, alleging the thieves had collected up to 188 credit cards using Cobain's identity, the New York Daily News reported Sunday.
"It was fraud after fraud," the 43-year-old rocker said. "But nobody believed me until now."
Love said she first learned of the identity scam in 2003, but personal issues kept her from stopping the illicit activities.
She said the thieves also purchased several cars and cashed checks using the identity of her late husband, who killed himself in 1994.
The Daily News said Cobain's estate earns more than $40 million a year thanks to the ongoing success of Nirvana, with most of that money being placed in a trust fund for the couple's daughter, Frances Bean.