Surgical robot research is driven by the desire of improving surgical outcomes. This paper proposed a Recurrent Neural Network based controller to address two problems: 1) improving control precision, 2) increasing adaptiveness for robot motion (explained in Section I). RNN was adopted in this work mainly because 1) the problem formulation naturally matches RNN structure, 2) RNN has advantages as an biologically inspired method. The proposed method was explained in detail and analysis shows that the proposed method is able to dynamically regulate outputs to increase the adaptiveness and the control precision. This paper uses Raven II surgical robot as an example to show the application of the proposed method, and the numeral simulation results from the proposed method and three other controllers show that the proposed method has improved precision, improved high robustness against noise and increased movement smoothness, and it keeps the manipulator links as far away as possible from physical boundaries, which potentially increases surgical safety and leads to improved surgical outcomes.