An exoskeletal robot can assist the movement of target joints effectively, but the eccentricity in the center of gravity caused by wearing an exoskeletal robot causes an imbalance problem. Such a side effect causes unnatural posture and additional effort for the wearer to maintain the body balance. To minimize the side effect, this paper proposes a control method of an exoskeletal robot to assist a certain target motion with body weight support and balance maintenance functions at the same time. The exoskeletal robot used in this study measures the center of pressure on the wearer's feet in real-time using air pressure sensors embedded in the soles of the shoes. Then the proposed control method determines the direction of the assistive force to assist the wearers balancing. The desired assistance torque required for realizing the proposed assistance method is precisely generated by series elastic actuators installed at the hip and knee joints of the exoskeletal robot. In the experiments, an assistance effect is verified by measuring the EMG signals of the six lower-limb muscles that are mainly involved in the target movement. This paper also introduces the experimental results that show the proposed assistive method reduces the EMG signal in five muscles, and reduces the variation of the COP movement compared to the case where only the body weight support method is applied in the control of the exoskeletal robot. These demonstrate that the proposed assistance method effectively assists in balancing and body weight supporting effectively.