The mission dubbed "Crew-4" took off from Kennedy Space Center, Florida, at 03:52 local time (07:52 GMT) with Americans Kjell Lindgren, Bob Hines and Jessica Watkins on board, as well as Italian Samantha Cristoforetti , from the European Space Agency.
The shooting was broadcast live on NASA's website.
SpaceX completed the launch less than 40 hours after picking up another crew, another acceleration in the flight schedule since Elon Musk's company became NASA's taxi to the ISS.
The four astronauts of "Crew-4" will join another crew which sees its return to Earth approaching after a five-month mission, and whose return date will soon be known.
Three Russians are also present on board the ISS.
The new crew will set up and monitor hundreds of experiments in weightlessness, notably on plants or an artificial human retina project.
Jessica Watkins will be only the fifth black woman to go into space, and the first to join the space station for a long mission.
She and her three crewmates are expected to reach the ISS around 17 hours after liftoff, with docking scheduled for 12:15 a.m. GMT on Thursday.
© 2022 AFP