The shaking force balancing is a well-known problem in the design of high-speed robotic systems because the variable dynamic loads cause noises, wear and fatigue of mechanical structures. Different solutions, for full or partial shaking force balancing, via internal mass redistribution or by adding auxiliary links were developed. The paper deals with the shaking force balancing of the Orthoglide. The suggested solution based on the optimal acceleration control of the manipulator’s common center of mass allows a significant reduction of the shaking force. Compared with the balancing method via adding counterweights or auxiliary substructures, the proposed method can avoid some drawbacks: the increase of the total mass, the overall size and the complexity of the mechanism, which become especially challenging for special parallel manipulators. Using the proposed motion control method, the maximal value of the total mass center acceleration is reduced, as a consequence, the shaking force of the manipulator decreases. The efficiency of the suggested method via numerical simulations carried out with ADAMS is demonstrated.