This paper proposes a tracking control method for a three-wheeled omnidirectional manipulator system (OMMS) with disturbance and friction. The OMMS is separated into two subsystems, a three-wheeled omnidirectional mobile platform (OMP) and a selective compliant articulated robot for assembly (SCARA) type of manipulator. Therefore, two controllers are designed to control the OMP and the manipulator system. Firstly, based on a kinematic modeling of the manipulator, a kinematic controller (KC), combined with an integral sliding mode controller (ISMC), is designed for the end-effector of the manipulator to track a desired trajectory with the desired angular velocity vector of links. Secondly, a differential sliding mode controller (DSMC) based on a dynamic modeling of the OMP with force external disturbances is proposed to obtain control inputs moving the OMP so that the manipulator tracks the desired posture without singularity. The system stability is proven using Lyapunov stability theory. The simulation and experimental results are presented to illustrate the effectiveness of the proposed controllers in the presence of disturbance and friction.