Halyna Hutchins died on the set of Rust in New Mexico after Mr Baldwin allegedly fired a prop gun.
Mr Baldwin, 64, was charged with involuntary manslaughter last month.
The family has been "devastated by the shocking killing" of Ms Hutchins, their attorney Gloria Allred said.
The suit, which alleges intentional infliction of emotional distress and negligence, is being brought in Los Angeles County Superior Court by Ms Hutchins' mother, father and sister, who are living in Ukraine, Ms Allred said during a news conference on Thursday.
