The spacecraft launched aboard a Falcon 9 rocket from Cape Canaveral, Florida at 1:52 am (0552 GMT).
"And Dragon is flying free, on its way to International Space Station," NASA commentator George Diller said.
It is scheduled to arrive at the ISS early Tuesday. The space station's robotic arm is to reach out and grapple the spacecraft at 7:04 am (1104 GMT), Diller said.
The journey to the ISS is the fifth for SpaceX, and the fourth in a series of SpaceX's contracted supply missions with NASA.
The supply ship is carrying 5,000 pounds (2,300 kilograms) of supplies, food and equipment -- including a 3D printer -- for the six-member crew at the orbiting outpost.
In 2010, SpaceX became the first private company to send a spacecraft to the ISS.
The company is run by Internet mogul Elon Musk, who accumulated his fortune by co-founding PayPal and also runs Tesla Motors.
Last week, SpaceX was awarded a USD 2 billion contract from NASA to continue developing its Dragon V2 vehicle with the goal of sending people to the space station as early as 2017.
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