As regards the impact and chattering of 4-DOF redundant parallel robots that occur under high-speed variable load operating conditions, this study proposed a novel control algorithm based on torque feedforward and fuzzy computational torque feedback hybrid control, which considered both the joint friction torque and the disturbance torque caused by the variable load. First of all, a modified dynamic model under variable load was established as follows: converting terminal load change to terminal centroid coordinate change, then mapping to the calculation of terminal energy, and lastly, establishing a dynamic model for each branch chain under variable load based on the Lagrange equation. Subsequently, torque feedforward was used to compensate for the friction torque and the disturbance torque caused by the variable load. Feedforward torques include friction torque and nonlinear disturbance torque under variable load. The friction torque is obtained by parameter identification based on the Stribeck friction model, while the nonlinear disturbance torque is obtained by real-time calculation based on the modified dynamic model under variable load. Finally, dynamic control of the robot under variable load was realized in combination with the fuzzy computational torque feedback control. The experimental and simulation results show that the motion accuracy of the fuzzy calculation torque feedback and torque feedforward control of the three drive joints of the robot under variable loads is 49.87%, 70.48%, and 50.37% lower than that of the fuzzy calculation torque feedback. Compared with pure torque feedback control, the speed stability of the three driving joints under fuzzy calculation torque feedback and torque feedforward control is 23.35%, 17.66%, and 25.04% higher, respectively.