This paper presents a method of simple adaptive control (SAC) for nonlinear systems using Elman recurrent neural networks (ERNNs). The control input is given by the sum of the output of a simple adaptive controller and the output of the ERNN. The ERNN is used to compensate the nonlinearity of plant dynamics that is not taken into consideration in the usual SAC. The role of the ERNN is to construct a linearized model by minimizing the output error caused by nonlinearities in the control systems.