In this paper, we propose a sliding mode controller for a robot manipulator with passive joints. A robot manipulator with passive joints which are not equipped with any actuators is a kind of underactuated system. Underactuated systems have some advantages compared to fully-actuated ones. For example, they weigh less and consume less energy because they have smaller number of components than fully-actuated ones. However the control of an underactuated manipulator is much more difficult than that of fully- actuated robot manipulator. In this paper a complex dynamic model of a manipulator with passive joints is manipulated for sliding mode control. Sliding mode controllers are designed for this complex system and the stability of the controllers is proved mathematically. Finally a simulation for this control system is executed for evaluating the effectiveness of the designed sliding mode controller.