In her complaint, the woman alleged that she had received a friend request from the accused on Facebook in December 2015 and she accepted it, after which they started meeting, they said in Delhi.
The victim alleged that the accused had assured her of marriage and that he would also accept her daughter, police said.
The woman claimed that she had two abortions on the insistence of the accused, they said.
The victim, who has separated from her husband, approached the police on July 10 and a case was registered at the Vasant Kunj Police Station. The matter is being probed, said the police.