The Falcon 9 rocket launched at 2:44 this morning, carrying the unmanned Dragon spacecraft filled with cargo.
It's the first time a private company will attempt to deliver goods to the ISS.
SpaceX CEO and Chief Designer Elon Musk says they still have to test the instrument bay doors and the sensors to make sure the Dragon will be able to lock on to the ISS.
"And then we're going to see how well those sensors are performing. Then in a few days we will do a fly-by of the space station and attempt to do the lockon with the sensors and do precision maneuvers relative to the space station."
On Friday, NASA engineers will decide if Dragon will be allowed to approach the station. If preliminary maneuvers are successful, the spacecraft will dock with the ISS for six days before returning to Earth.
NASA's Associate Administrator for Human Exploration Bill Gerstenmaier says if things go well on this mission, NASA is prepared to immediately start using commercial rockets to deliver all cargo to the ISS.
"We'll take a look at how the mission goes and if we think the failure is small enough and can be easily corrected, then we could go right into commercial supply services and we wouldn't need to do another demonstration flight. If it's something that we collectively think requires a lot of extra work and would actually benefit from another test flight, then we would go propose a test flight."
SpaceX is also working with NASA to develop a private spacecraft that could carry seven astronauts to and from the ISS.