Because of their mechanical properties, parallel mechanisms are most appropriate for large payload to weight ratio or high-speed tasks. Cable driven parallel robots (CDPRs) are designed to offer a large translation workspace, and can retain the other advantages of parallel mechanisms. One of the main drawbacks of CD-PRs is their inability to reach wide ranges of end-effector orientations. In order to overcome this problem, we introduce a parallel spherical wrist (PSW) end-effector actuated by cable-driven omni-wheels. In this paper we mainly focus on the description of the proposed design and on the appropriate placement of the omni-wheels on the wrist to maximize the robot dexterity.