Grigorieva, 40, told People magazine she was holding their baby, Lucia, when Gibson, 56, assaulted her.
"I thought he would kill me," Grigorieva said.
The musician went on to say she taped Gibson's angry phone calls because she feared for her and her child's safety. She also denied leaking the audio to media outlets.
"I needed to document his threats," she explained.
People magazine said Gibson declined to comment on its story.
He has in the past, however, denied allegations he threatened or assaulted her and has said his ex-girlfriend tried to extort money from him.
A source close to Gibson told the magazine the alleged altercation Grigorieva is talking about took place as Gibson intervened when Grigorieva was shaking their baby.
Copyright 2010 United Press International, Inc. (UPI).