The International Space Station has four astronauts on it.
The men are called the Axiom-1 crew. The company hopes to build a space station in the next few years.
The crew lifted away from Kennedy Space Center at 11:17 local time.
The station is expected to receive their capsule on Saturday.
A former US space agency astronaut is in charge of the mission.
US real estate mogul and aerobatic pilot Larry Connor is one of the people flying with him.
They will spend eight days on the International Space Station, conducting scientific research and doing a number of outreach projects.
The company was founded in 2016 to exploit the emerging market for commercial activities in low Earth orbit.
The firm is planning a number of similar missions. The next one will be in early or late 2023. A crew member will be chosen through a reality TV series.
The company has an agreement with Nasa to add its own modules. The idea is that the modules will bud off on their own to become a private space destination before the International Space Station is retired.
While Russia allowed private astronauts to visit the station as far back as 2001, Nasa resisted the practice until announcing a change in policy in 2019.
The agency is charging a fee for the use of the space station. The capability to return certain scientific samples back to Earth is being purchased by Nasa.
The second private spaceflight was conducted by American rocket and capsule supplier SpaceX. Last year it sent up a mission. This was bought by a billionaire. He and his three crewmates were in space for almost three days.