The workspace of manipulator can be defined as the operational area of the end effector. Because the moving platform of the parallel manipulator with six degree-of-freedom have six independence degree-of-freedoms, it means the workspace has six-dimensional, the six-dimensional workspace is difficult to be directly calculate and unable to graphic description. For the project of this article--3/3-RRRS parallel manipulator, this article will analyze the workspace of the manipulator in two cases. A discretization method is proposed for the computation of the reachable position/orientation workspace of the 3/3-RRRS parallel manipulator, respectively. Four examples of a 3/3-RRRS parallel manipulator are given to demonstrate these theoretical results. As a special position and inherent attributes of the mechanism, singularity has a serious impact on the mechanism’s motion control performance and drive performance. The method of searching algorithm in three-dimensional space is applied to the singularity analysis, coordinate of all possible stable positions are substituting into the Jacobian, position-singular points under given orientation condition are conformed.