Stormy Daniels says the agreement, drawn up before the 2016 election, is “void” because he did not sign it.
Mr Trump’s personal lawyer, Michael Cohen, confirmed last month he had privately paid her $130,000 (£95,000).
The lawsuit alleges that Mr Cohen tried to “intimidate her into silence.”
In a 2011 interview with InTouch magazine, the actress said she began a sexual relationship with Mr Trump in 2006, shortly after his wife Melania had given birth to his son Barron.
The reports re-emerged in January when the Wall Street Journal reported that she was paid to sign a non-disclosure agreement in the run up to the 2016 election, which prevented her from discussing the alleged liaison.
Mr Cohen has said the president “vehemently denies” any romantic involvement with the adult film star,
The civil lawsuit, filed in Los Angeles on Tuesday, says that only days before the election, Ms Clifford and Mr Cohen signed the “hush agreement” but Mr Trump did not, “thus rendering it legally null and void and of no consequence”.
It adds: “To be clear, the attempts to intimidate Ms Clifford into silence and ‘shut her up’ in order to ‘protect Mr Trump’ continue unabated.”
Although Mr Cohen confirmed that he paid the money to Ms Clifford, he did not say what it was for.
He said last month that neither Mr Trump nor the Trump Organization was a party to the transaction.
“The payment to Ms Clifford was lawful, and was not a campaign contribution or a campaign expenditure by anyone,” he said. (Courtesy BBC)