PID control is widely used in industrial areas, but it is not easy to tune PID gains for an optimal control. The proposed learning method is to tune PID gains using the gradient approach. We use two estimation functions in this method : one is an error function for tuning of PID gains, and the other is a performance measuring function for a completion of learning. This paper shows that optimal PID controllers can be acquired when this learning method is applied to 10 systems with different natural frequencies and damping ratios.