The incident involving seven people on the Cessna aircraft happened just before 12:30 p.m., according to Bill Begley, spokesman for the Houston Airport System.
The jet suffered a brake failure, causing it to run off the runway and come to a rest in the grass.
Begley said there was no damage to the the plane.
The plane flew from Pueblo Memorial Airport Sunday, and was scheduled to fly to Aspen, Colorado at 6:36 p.m. Tuesday night.