Chloe Goins claims Mr Cosby drugged and molested her when she was 17.
The civil lawsuit accuses Mr Cosby of "childhood sexual abuse" and demands damages of at least $75,000 (Â£49,000). Ms Goins is also seeking a jury trial.
Mr Cosby, 78, is facing a series of sexual assault accusations dating back decades. He has denied the claims.
The star is due to testify on Friday in a separate lawsuit brought by Judy Huth, who accused the comedian of sexually abusing her at the Playboy Mansion in 1974, when she was 15 years old.
More than 50 women have come forward publicly over the past year with allegations including drugging, sexual harassment, sexual assault and rape - all of which Mr Cosby denies.
In most cases, the alleged incidents date back decades, meaning they fall outside the time limit for legal action.
But Ms Goins' allegations do fall within California's statute of limitations, and prosecutors are also now reviewing the evidence for possible criminal charges.
The model told reporters: "Today I recognise that I've taken legal action that many of the other victims of Bill Cosby will never be able to take. This has gone on long enough, it's time Bill Cosby was held accountable for his crimes."
Ms Goins' lawyer Spencer Kuvin said the alleged assault happened before her 18th birthday in May 2008. Cosby's lawyer Marty Singer has previously claimed she was referring to an event at the Playboy Mansion that August.
Mr Cosby's spokesman Andrew Wyatt declined to comment to the Reuters news agency on Tuesday about Ms Goins' lawsuit.
A 25-year-old model has sued US comedian Bill Cosby, alleging he sexually assaulted her at the Playboy Mansion in Los Angeles in 2008.