Aiming at the complexity of selecting interpolation points in robot joint space trajectory interpolation, a trajectory interpolation method based on trajectory compression was proposed based on the gate-shaped trajectory of the Delta robot moving platform. The PH curve was adopted to smooth transition trajectory of the moving platform in the corner, arbitrary trajectory point location was represented by the rotation angle of the three driving rods, forming joint space trajectory. Combining genetic algorithm and the improved TDTR algorithm, the trajectory of the active rod rotation joints was offline compressed, getting characteristics of track points as five NUBRS path interpolation. The interpolation points were compared with the same number of trajectory points evenly divided by time and distance. It is proved that the maximum angular velocity and acceleration of joint are reduced by trajectory interpolation based on trajectory compression. The co-simulation results show that this method reduces the maximum acceleration of the moving platform. The test results verify the simulation conclusion that the moving platform is stable and the rate of cyclic picking operation can reach 50 times/min, which proves that the method has advantages in improving the motion stability.