The paper presents a model predictive trajectory tracking controller for a five degree of freedom hybrid robot for milling. The construction of the manipulator is introduced, forward and inverse kinematics problems are solved in a closed analytical form, a simplified dynamic model, suitable for control synthesis is described. Control law of the computed torque type is proposed with modifications that improve the performance of trajectory tracking. The control algorithm is tested in experiments conducted on a robot material prototype without actual milling. The presented results are very good for the parallel part of the robot, but require improvement for the serial part. Finally, the conclusions and indications towards future investigations are presented.