Motion control of mobile manipulators (a robotic arm mounted on a mobile base) can be challenging for complex tasks such as material and package handling. In this paper, a task-space stabilization controller based on Nonlinear Model Predictive Control (NMPC) is designed and implemented to a 10 Degrees of Freedom (DOF) mobile manipulator which consists of a 7-DOF robotic arm and a 3-DOF mobile base. The system model is based on kinematic models where the end-effector orientation is parameterized directly by a rotation matrix. The state and control constraints as well as singularity constraints are explicitly included in the NMPC formulation. The controller is tested using real-time simulations, which demonstrate high positioning accuracy with tractable computational cost.