The workspace of parallel robot is limited, and the distribution characteristics of kinematics and force maneuverability are complex in the workspace. In addition, there are often operational singularities. The redundant actuation technology can not only overcome singularity problem of force maneuverability of parallel mechanism, but also eliminate the clearance of the mechanism, dynamically adjust the operating stiffness, realize the optimized operation of energy consumption, etc. In this paper, with the goal of realizing dexterous dynamic output control, the variable impedance control technology of redundantly actuated parallel robot based on operation space is studied. Compared with the traditional invariable impedance control, the variable impedance control can adapt to the change of unknown environment by time-varying controlling parameters, which provides the possibility to realize the polishing of complex curved surfaces and thin-walled parts, assembly task and improves the performance of the system and the machining quality of the parts. In order to avoid the influence of unmodeled errors and external interferences on the system, based on the sliding mode control (SMC) strategy, the variable impedance control (VIC) in the operating space of 4RRR redundantly actuated parallel robot (4RAPR) is proposed. The robust stability of the closed-loop system is analyzed and verified by Matlab programming simulation.