The concept of two-wheeled mobile manipulator (TWMM) has been proposed for its significant advantage due to high maneuverability particularly in confined internal spaces. However, its unbalanced structure imposes restrictions for widespread application. Note that the nonholonomic property of a TWMM makes its control a more challenging task. In this paper, a new stabilization mechanism of TWMM is presented, and a new control method based on dynamical balancing algorithm is proposed that could effectively resolve those restrictions. To this end, a reaction wheel is considered to control the position of center of gravity (COG), leading to a smoother motion of the robot manipulator. To make the robot be able to manipulate an object, a double inverted pendulum model (DIPM) is considered as a simplified model of the system. DIPM dynamics is used to identify and simplify the dynamics of TWMM and subsequently a supervisory control is employed to stabilize the robot via its COG position. This in turn improves the robustness of the proposed algorithm during manipulation maneuver of an object with unknown mass parameters. Results are compared to those of an ideal model-based algorithm that reveal the merits of the proposed control strategy.