Falcon 9 lifted off on Saturday, local time, from Kennedy Space Center in Florida.
Attached was the Dragon capsule, carrying two astronauts from NASA, and the capsule successfully separated from the rocket and reached orbit.
This is the first time the U.S. has sent astronauts into space from its own soil in nearly a decade.
During that time, the U.S. had to rely on Russia to reach space at a cost of up to 90 million U.S. dollars a seat.
The two astronauts, Doug Hurley and Bob Behnken, are experienced, having each been into space twice, but this trip is different.
The capsule's interior has touch screens like those on Tesla cars, and it has auto-pilot.
When needed, though, the astronauts can take over.
President Trump praised the launch and looked forward to more developments.
"We have created the envy of the world, and will soon be landing on Mars and will soon have the greatest weapons ever imagined in history -- I've already seen designs, and even I can't believe it. The United States has regained our place of prestige as the world leader. As has often been stated, you can't be number one on Earth if you are number two in space"
Elon Musk founded SpaceX in 2002 with the dream of reaching Mars.
The company, along with Boeing in 2014, was awarded a contract to carry humans into space, which at the time was a mission doubted by many.
Now, it has become the first private company to achieve that.
After the Dragon capsule separated, Falcon 9 successfully returned to earth and landed on its launch pad, and the astronauts are expected to reach the International Space Station by 11 PM Sunday, Korea time.
Kim Do-yeon, Arirang News