Gabbard's campaign filed the lawsuit claiming in the hours after the first Democratic Presidential Debate last month, the tech giant suspended her Google ads without notice.

Gabbard says her campaign worked frantically to find out why, but she claims Google fed her BS answers and to date has "not provided a straight answer or let alone a credible one."

Gabbard -- an Iraq War veteran -- says the suspension came at the most crucial time in her campaign ... because immediately after her performance at the debate, Gabbard became the most searched candidate after entering relatively unknown.

Making matters worse ... Gabbard claims Google's sending campaign emails into people's spam folders. She says this is not happening with other candidates and calls it censorship.

Gabbard's suing because she says it's a violation of her First Amendment rights.

We've reached out to Google, and a spokeswoman tells TMZ ... the search engine has "automated systems that flag unusual activity on all advertiser accounts -- including large spending charges -- in order to prevent fraud and protect our customers."