Nick Carter is being sued by a woman who says he raped her and infected her with a bunch of sexually transmitted diseases … but he says her allegations are bogus.

The Backstreet Boys singer is being sued by a woman named Laura Penly, who claims he sexually assaulted her multiple times.

In the lawsuit, obtained by TMZ, Penly claims she met Nick in 2004 when she was 19 years old and they started banging for a couple weeks … meeting up at a Los Angeles apartment to hang out and have sex. She says she asked him to wear a condom but he refused and told her he was “clean” from STDs.

She claims she never had unprotected sex before meeting Nick. She says she came over once in early 2005 and told Nick she didn’t want to have sex … but she says he responded by telling her the only reason she was there was to have sex with him.

Penly claims Nick then picked her up off the ground, threw her onto his bed, bent her over the side of the bed and forcefully penetrated her vagina with his penis despite her telling him “no” multiple times. She says he didn’t wear a condom during the alleged assault.

She claims Nick told her to keep the sexual assault a secret because no one would believe her … and she says a couple months later he apologized and asked to see her again.

Penly says she visited Nick in L.A. again and he led her into his bedroom, where she told him she didn’t want to have sex. She claims he proceeded to forcefully penetrate her and ignored her repeated refusals and requests for him to stop.

The woman claims Nick infected her with various STDs … including HPV. She says she tested positive for chlamydia and gonorrhea and was told she was diagnosed with cervical cancer, which she says is a result of the HPV infection.

Penly says she had to undergo cancer treatments, including surgery … and she says the alleged sexual assaults caused her severe emotional distress, physical anguish, medical issues, intimacy issues and other trauma.

She’s suing Nick for sexual assault and intentional infliction of emotional distress, negligent infliction of emotional distress, and she’s going after him for damages.

Liane K. Wakayama and Dale Hayes Jr., attorneys for Nick, tell TMZ … “This is just more of the same nonsense from the gang of conspirators and their lawyers who continue to abuse the justice system to try to ruin Nick Carter. It’s drawn from the same predictable playbook – lie in wait for decades until Mr. Carter is celebrating a professional milestone, then hide behind litigation privilege to make utterly false claims in an attempt to inflict maximum damage on Nick and his family.”