"My wish is to go up on the 50th anniversary of the moon landing, that's what we're working on," the head of the Virgin group said on the sidelines of an event to honor Virgin Galactic at the Air and Space Museum in Washington.
The American Apollo 11 mission landed on the moon July 20, 1969.
Virgin Galactic is one of two companies, along with Blue Origin, on its way to sending passengers into space—though just barely, and just for a few minutes.
The companies want to send hundreds or thousands of people on these short "suborbital" flights, meaning they wouldn't get high enough to orbit the earth.
These missions would be shorter and more affordable than SpaceX's planned project to send a Japanese billionaire to the moon by 2023 at the earliest.
Virgin Galactic flew 50 miles (80 km) above the earth, which the US considers the edge of space, for the first time in December (the international consensus is 100 km).