"Starship should be able to make it to the moon in less than five years," Musk said on his social media platform X.
SpaceX will also take astronauts furthest they have been past half a century during this year, Musk added.
In January, Musk said he hopes his company will send humans to the Moon and Mars within the next eight years.
Musk also announced plans to colonize Mars and has built the Starship spacecraft to achieve that goal.
In addition, Musk has announced plans to send one million people to Mars by 2050. Industry experts call such a goal unrealistic.