The astronauts are unloading a half-ton of cargo that includes food, clothes, batteries and some student science experiments.
One astronaut said the capsule has that "new car smell."
"The smell inside smells like a brand new car," reported NASA astronaut Donald Pettit. The compartment was brilliantly white and, he noted; clean, no dirt or other particles appeared to be floating around.
SpaceX is the first private company to send a vessel to the space station. It's run by Elon Musk, a billionaire who helped create PayPal and founded the electric car company Tesla Motors.
NASA is turning over orbital delivery work to American businesses so it can focus on getting astronauts to asteroids and mars. The space agency hopes astronaut ferry trips will follow soon; SpaceX contends its Dragons could be carrying space station astronauts up and down within three or four years.
The ship carried up 1,000 pounds of food, clothes, batteries and other provisions. It will bring back 1,400 pounds of gear.
The Associated Press contributed to this report.