In this paper we propose a fast and precise control algorithm for a mobile robot, which aims at the self-tuning control applying two multi-layered neural networks to the structure of computed torque method. Through this algorithm, the nonlinear terms of external disturbance caused by variable task environments and dynamic model errors are estimated and compensated in real time by a long term neural network which has long learning period to extract the non-linearity globally. A short term neural network which has short teaming period is also used for determining optimal gains of PID compensator in order to come over the high frequency disturbance which is not known a priori, as well as to maintain the stability. To justify the global effectiveness of this algorithm where each of the long term and short term neural networks has its own functions, simulations are peformed. This algorithm can also be utilized to come over the serious shortcoming of neural networks, i.e., inefficiency in real time.