A mobile manipulator is a hybrid of a wheeled vehicle and a robotic arm realizing large locomotion and handling operations that cover many robotic applications, including housework, cleaning, and construction. A mobile base generally achieves large movement but coarse positioning accuracy, whereas a robotic arm only realizes high-precision manipulation within its reach. The present paper introduces a model predictive control (MPC) for mobile manipulators exploiting the advantages of a mobile base and a manipulator while their drawbacks are compensated. We take advantage of the high mobility of the mobile base and high accuracy of the manipulator by incorporating state-dependent velocity constraints into the MPC. If a mobile manipulator is far from the target, then the MPC drives the mobile base to the area where the manipulator can reach the target while suppressing the unnecessary motion of the manipulator. When a mobile manipulator arrives at the operation range, the motion of the mobile base is suppressed to prevent disturbing the manipulator by slippage or disruptive motion of the wheels. We evaluated the performance of the controller in the multi-body dynamics simulator for the two scenarios requiring locomotion and manipulation. The results were compared with a conventional MPC to demonstrate the effectiveness of the proposed controller.