The company's Falcon 9 rocket blasted off at 2AM (0600 GMT) carrying the EchoStar XXIII, a commercial communications satellite for EchoStar Corporation.
The satellite will be placed in orbit more than 35,000 kilometres above the earth and provide telecommunications service to Brazil, SpaceX said.
However, SpaceX said it will not attempt to land Falcon 9´s first stage after launch "due to mission requirements."
The mission took off from NASA´s historic launch pad 39A, the origin of the pioneering US spaceflights that took astronauts to the Moon in the 1960s and 1970s, as well as the space shuttle missions that ran from 1981 to 2011.
SpaceX, founded and led by billionaire Elon Musk, is emerging as a leader in the modern commercial space industry after becoming the first to send a private cargo carrier to the International Space Station in 2010.
The California-based company has endured two costly disasters in the past two years -- a launchpad blast that destroyed a rocket and its satellite payload in September, and a June 2015 explosion after liftoff that obliterated a Dragon cargo ship packed with provisions bound for the space station.