This research concerned about an online learning algorithm of the group method of data handling based proportional-integral-derivative (GMDH-PID) controller that is effective for nonlinear systems. Although a lot of PID controllers have been mainly used in industrial systems, it is difficult to maintain a desired control performance only by a PID controller with fixed control parameters due to system nonlinearities. In order to deal with such systems, a GMDH-PID controller that can adjust PID parameters according to a system change was proposed, and its effectiveness was evaluated. The GMDH-PID controller can maintain good control performance by appropriately setting its weight coefficients in the GMDH network. However, these coefficients are determined in an offline manner, thus the GMDH-PID controller cannot adapt a system if unexpected system change is happened while controlling. This paper proposes an online tuning method of the GMDH-PID controller based on the adaptive moment estimation that is one of recent attracted optimization methods. Thanks to this method, the GMDH-PID controller can adapt to unknown system change, thus applicable rage of the controller is expanded. The effectiveness of the proposed method is demonstrated by simulation examples.