This paper presents a singularity study on a special class of spatial cable-suspended parallel mechanisms (CSPMs) with merely three translational degrees of freedom using redundant actuators. This paper focuses on the CSPMs that have the capability to perform the purely translational movement with pairwise cables as parallelograms. There are two types of singularity to be discussed, which result from dynamic equations of CSPMs and the parallelogram constraint of pairwise cables. To ensure three-translational dofs without rotation of the end-effector, the matrix formed by normals of the planes based on each pairwise cables should maintain in full rank. In the case study, four typical designs of CSPMs with a planar end-effector and a spatial end-effector are discussed to clarify and conclude the singularity features of CSPMs with actuation redundancy. The results show that for some architectures there exist both types of singularity for redundantly actuated CSPMs with pairwise cables but for some other architectures the redundant actuation exerts no effect on the singularity issue.