In the recordings, first reported by TMZ.com, the Australian-raised Oscar winner allegedly uses a highly offensive term levelled against African Americans.
"You look like a f...ing pig in heat and if you get raped by a pack of n.....s it will be your fault," Gibson allegedly screams at Grigorieva, according to TMZ.
TMZ says it has confirmed it is Gibson on the tape, which Grigorieva secretly recorded.
The former couple is in the midst of a bitter custody battle for their baby daughter, Lucia, and the secret recordings have been submitted to the Los Angeles judge overseeing their case.
In 2006 Gibson's image and career took a major hit when he was arrested at Malibu for drink driving and went on an anti-Semitic rant, saying, "F...ing Jews.... The Jews are responsible for all the wars in the world."
The anti-Semitic comments were condemned by religious leaders and high-powered members of Hollywood, but in the years since, Gibson has worked hard to repair his battered reputation.
The latest tirade quickly drew fire from the National Association for the Advancement of Colored People (NAACP), with the organisation's LA president, Leon Jenkins, saying it is unfortunate Gibson "has made his millions off of women, African-Americans and Jews", but harbours "such racist, sexist, and anti-Semitic feeling against people who have admired and respected him for decades".
"An apology is insufficient given his history of racism, sexism and anti-Semitism," Jenkins told TMZ.
"No amount of words will change his image as an out-of-date and out-of-control racist. "Only by a sustained period of positive acts can his legacy be redeemed."
Gibson's Australian wife of 30 years, Robyn Moore, filed for divorce in April last year citing irreconcilable differences.
On October 30, Grigorieva gave birth to Lucia, Gibson's eighth child.
Attorneys for Gibson and Grigorieva have concluded a closed-door hearing with a judge handling their child custody case.
Attorneys for the actor-director and Russian singer declined to comment on the case, which remains sealed.
The couple split in April. Gibson's attorney, Stephen Kolodny, says the former couple entered into a confidential agreement a month later. A child custody case was filed in Los Angeles last month, but those records are sealed.
Neither Gibson or Grigorieva, attended Thursday's hearing.
Kolodny has said Gibson has provided his ex-girlfriend with substantial support. Grigorieva said in a statement that she could not discuss the case.
