This paper presents dynamic modeling and attitude and motion control of Free-Flying Space Robots (FFSR) in the absence of external forces and torques. Instead of thrusters, electrically powered reaction wheels are utilized to provide accurate and continuous torque. Referring to the dynamic model of the space robot system, a Nonlinear Model Predictive Control (NMPC) algorithm is developed in the task space to control the attitude of the spacecraft and the end-effector motion. The performance of NMPC is compared with that of Sliding Mode Control (SMC). The effectiveness of the proposed control algorithm is verified by simulations. When the system uncertainties are not considered, the proposed NMPC application demonstrates higher accuracy than SMC and it can be achieved without the need to linearize the dynamic equations of the FFSR.