Robotic assistance is promising for improving minimally invasive surgery (MIS). This work presents asymmetric bimanual control of a dual-arm serial robot with two remote centers of motion (RCMs) constraints for MIS. In our previous works, general null space controllers to guarantee the fixed RCM constraint have been proposed. However, an incision on a patient’s abdominal wall is not fixed owing to the respiration of the patient, which generates an uncertain disturbance at the joints of robotic manipulators. To improve accuracy, a radial basis function neural network is implemented to adapt to these disturbances and control the end-effector position. Finally, the adaptive bimanual control strategy is validated through simulations based on clinical data. The proposed control shows improved accuracy in the end effector position for all the designed surgical tasks. In future works, the algorithm will be validated on an actual dual-arm serial robot making use of a body phantom.