In underactuated robots (URs), the motion of the unactuated configuration variable is coupled to that of the others by complex dynamics, which makes their control complicated. Additionally, if the UR is a cable-driven robot (CDR), as cables merely support tensile force, the positiveness of the cable’s tension should also be taken into account in controller design. In this paper, we investigate the regulation control of a suspended three degrees of freedom (DOF) CDR using interconnection and damping assignment passivity-based control (IDA-PBC) via potential energy shaping. This method requires analytical solutions to a set of partial differential equations (PDEs). The IDA-PBC approach for the control of the three-DOF CDR results in a complex PDE that cannot be analytically solved using the proposed methods in the literature. To this aim, we transform the governing PDE into a number of Pfaffian differential equations. Then, the resultant Pfaffian equations are solved analytically to obtain the homogeneous solutions of the PDE. Additionally, we have also considered the positiveness of the cables’ tension by suitably defining the parameters of the controller. The efficacy of the proposed controller is investigated through simulation, and its performance is compared with a sliding mode control approach.