Attorney Willie E. Gary filed the lawsuit on behalf of Joanna Johnson, who will be the executor of the estate of Lonnie Jordan. Jordan was one of 33 people on board the El Faro as it sailed toward Puerto Rico two weeks ago. The ship disappeared somewhere near the Bahamas, the U.S. Coast Guard has said.
"Money won't bring him back, I know that. But we're going to change things and that's what big business understands is when you hit them in their pockets," Gary told reporters.
Gary alleged that the 40-year-old El Faro wasn't seaworthy and that ship owner Tote Services and Tote Maritime Puerto Rico was greedy. He said there was another ship available and the company should have sacrificed profits in the name of safety.
Tote Services has said that while the maritime accident is being investigated, it cannot comment on El Faro's disappearance. CNN reached out to the company for comment on the lawsuit but didn't immediately hear back.
Tote has said Capt. Michael Davidson had a "sound plan" to avoid Hurricane Joaquin, a strategy that only unraveled when the ship's main propulsion stopped working.
Hurricane Joaquin had 140 mph winds as it strafed the Bahamas and produced 50-foot high waves.
Authorities have found one body and debris but called off the search last week.
Gary's motion allows his law firm to begin the process of discovery. He indicated he would have other clients who would sue, but wanted to get started on the case.
"We're going to move as expeditiously as possible," he said. "We're not going to let our cases sit around and our families suffer."