This work is focused on the motion control of an underactuated brachiation robot with 3 links. We present the modeling of the dynamics of the robot and introduce the application of the model-based predictive control (MPC) using a linearized model of the system. The robot has 3 revolute joints but only one of them is actuated, i. e., the robot has less control inputs than degrees of freedom. The investigation of the MPC to control such a system is due to the fact that MPC is able to deal with constraints (state or input limitations) in a direct way, obtaining an optimal control law. Also, it is investigated the use of a linearized model for prediction of system state. Simulation results are shown for complete arm switching, as well as some directions for future developments. Keywords— Brachiation Robot, underactuated systems, Linearized Model Predictive Control.