PID controller has been widely used in industry. Because it has a simple structure and robustness to modeling error. But it is difficult to have uniformly good control performance in system parameters variation or different velocity command. In this paper, we propose an adaptive PID controller based on a gradient descent learning. This algorithm has a simple structure like conventional PID controller and a robustness to system parameters variation and different velocity command. To verify performances of the proposed adaptive PID controller, the speed control of nonlinear DC motor is performed. The simulation results show that the proposed control systems are effective in tracking a command velocity under system parameters variation.