The dummy pilot is a mannequin nicknamed "Ripley" after Sigourney Weaver's character in the Alien films.
The mission is a test launch with only a dummy on board the capsule before a manned flight set for later in 2019.
The first American commercially built-and-operated crew spacecraft in eight years docked successfully Sunday at the International Space Station.
The launch is a milestone for Elon Musk's space company and NASA's long-delayed goal to resume human spaceflight from USA territory later this year. That's the part of the uncrewed test run that concerns SpaceX CEO Elon Musk the most, the BBC wrote.
Behnken said he was "super excited" by the Dragon successfully docking at the ISS.
For SpaceX, which Musk founded in 2002, sending an astronaut into orbit would be a culmination of years of hard work and high-risk investment.
It's a six day mission in the Crew Dragon is scheduled to splash back down to earth next Friday morning.
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"Congratulations to all nations, private space firms and individuals who wake up every day driven by the magic of exploration", American astronaut Anne McClain, the third crew member on the station, said at a welcoming ceremony broadcast over NASA TV.
In 2014, the USA space agency awarded contracts to SpaceX and Boeing for them to take over this task.But the program has suffered delays as safety requirements are much more stringent for manned flights than for unmanned missions to deploy satellites.
The Crew Dragon is carrying about 400 pounds of supplies and equipment for the three astronauts aboard the International Space Station. Astronauts have been stuck riding Russian rockets ever since NASA's space shuttle program ended in 2011.
"I fully expect we're going to learn something on this flight", said Bill Gerstenmaier, Nasa's head of human spaceflight.
SpaceX's Crew Dragon began its inaugural test flight early Saturday morning. But that quickly changed once the hatch swung open and the space station astronauts floated inside. In a docking with a crew aboard, the capsule would likewise operate autonomously, though the astronauts might push a button or two and would be able to intervene if necessary. Coincidentally, that adapter was delivered by a non-Crew SpaceX Dragon spacecraft.
The crew capsule is based on the ISS cargo freighter but incorporates life-support systems and more powerful thrusters to push the vessel to safety if something goes wrong with the rocket.
Eleven minutes into the flight, the Dragon is let go and must make its own way to the station.