The incident happened Saturday night while the family was having dinner outside on the Venice restaurant patio.
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Riley Pegram, the girl's father, said the man repeatedly walked up to them and tried taking the girl from her mother's arms, claiming that he had to "save her."
When he returned for the final time, Pegram's brother can be seen on surveillance video grabbing the suspect by the hair and throwing him backwards on the ground.
They say it's clear the man wasn't in his right mind.
"We think he was on something. On some type of drugs or something. I don't know if he was homeless but I know he was on drugs," Riley said.
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The pair held the man down until police arrived and said it took six officers to finally arrest him.
"They got him down, but the whole time he was just yelling out loud, 'Save the girl, I need to save her'," Riley added.
The suspect, identified as Evan McLaurin-Nelson, is a former Las Vegas resident who moved to California three years ago and is believed to be homeless, according to detectives with the Los Angeles Police Department. He has an arrest record in both states that includes battery, indecent exposure and disorderly conduct.
The Los Angeles County District Attorney's Office filed one count of attempted kidnapping and one count of resisting a peace officer against McLaurin-Nelson.