It is the first time that the company has flown a Falcon 9 rocket and Dragon spacecraft that have both been used before.
The recycled rocket doesn't add any extra risk, according to NASA's International Space Station manager, Kirk Shireman.
But the launch was "still a dangerous business", he said, and although the Falcon 9 has been extensively inspected by NASA's experts, there is never "zero risk" when it comes to rocket launches.
Minutes after launch, the Falcon 9 first stage landed successfully after delivering the Dragon into orbit. Its landing back at Cape Canaveral marked SpaceX's 20th recovery of a first stage booster.
This was the thirteenth of up to 20 missions to the International Space Station that SpaceX is contracted to fly for NASA.
Its Dragon capsules are not currently able to deliver crew to the ISS and are only being used to deliver cargo at the moment, although SpaceX is developing a variant for crew transport.
With this mission, SpaceX delivered about 4,800 pounds of cargo and material to support science investigations aboard the space station.
The Dragon was confirmed to be in good orbit, SpaceX announced on Twitter.
"After about one month attached to the space station, Dragon will return with results of earlier experiments, splashing down in the Pacific Ocean off the coast of Baja California."
The company, which is owned by billionaire Elon Musk, said the weather was 90% favourable for the launch on Twitter.
Mr Musk has said that his aims for SpaceX include assisting the colonisation of Mars.
It has broken new ground in aeronautics by recycling its Falcon 9 rockets and Dragon capsules.
Where its competitors' are forced to build new ones for every launch, SpaceX has managed to achieve an economy of business by reusing previously developed craft.
This has helped the company to be valued at $21bn (£16bn), making it one of the most valuable privately owned companies in the world.