The tech entrepreneur's company will launch a Falcon 9 rocket to transport NASA astronauts Bob Behnken and Doug Hurley in a first for the space agency as it looks to cut costs.
"NASA and SpaceX are currently targeting no earlier than mid-to-late May for launch," the US space agency said in a statement Wednesday.
In March, Musk's Crew Dragon capsule made a round trip to the ISS, which is in orbit more than 250 miles (400 kilometers) above Earth, with a mannequin on board, before returning to the Atlantic after six days in space.
Since the last US space shuttle mission in 2011, after 30 years of service, only the Russians have been going back and forth to the ISS.
SpaceX has made the trip 15 times since 2012, but only to refuel the station.
It is not the only private company servicing NASA: Boeing has also won a contract and is developing its own Starliner capsule.
