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The redundancy feature of the parallel mechanism can increase the effective workspace，realize the fault-tolerant motion，which improves the performance of the parallel mechanism. Based on the 3-PRS parallel mechanism structure characteristic，starting from the configuration of a kinematic sub-branches，a redundant kinematic sub-branches is designed，and then a 3-PR（P）S redundant parallel mechanism is proposed. The degree of freedom of 3-PR（P）S redundant parallel mechanism is analyzed by using screw theory，a kinematic model is established，and the kinematic equation is derived. Aiming at the problems of rough boundary and low accuracy in solving the workspace of parallel mechanism by classical Monte Carlo method，a Monte Carlo method based on boundary extremum densification is proposed. The workspace of 3-PR（P）S redundant parallel mechanism is analyzed，and specific solving steps are given. Finally，the workspace of 3-PRS parallel mechanism and redundant parallel mechanism under different parameters are figured by Matlab programming and simulation. The results show that the workspace of the 3-PR（P）S redundant parallel mechanism is greatly improved compared with the 3-PRS parallel mechanism under the same parameters，which provides a theoretical basis for trajectory planning and fault-tolerant control.