This paper proposes a mobile parallel robot (MPR) and focuses on obstacle avoidance. When analyzing the collision-free trajectories, the coupling constraints caused by the parallel mechanism and the obstacle should be emphatically solved. The solution is to divide the problem into two steps. First, the genetic algorithm is employed to search and optimize the feasible trajectories under the mechanism constraint of the MPR. Then the trajectory tracking controller is designed to make the tracked vehicles move cooperatively and track a trajectory asymptotically. Finally, simulations and experiments are carried out to verify the effectiveness of the solution.