Cable-Suspended Parallel Robots (CSPRs) utilize winches and cables as the actuation scheme instead of rigid links, which renders them advantages of both parallel mechanisms and cable mechanisms. In this paper, a robust sliding mode controller was designed for a three-degree-of-freedom CSPR with uncertain end-effector mass and external disturbances. To control the motions of CSPRs is usually challenging due to the unidirectional constraints of cable tensions. Based on interval analysis, a set of analytical inequalities is obtained which establish the relationship between the cables’ tension constraints and the controller parameters. The sufficient conditions of the controller parameters satisfying the constraints are obtained for the set-point motion subject to uncertainties. Numerical simulations are presented to verify the effectiveness of the proposed approach.