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This paper proposes an SAC using neural networks with offset error reduction for MIMO nonlinear systems. In this proposed method, the control input for the nonlinear plant is given by the sum of the output of a simple adaptive controller and the output of neural networks. The role of neural networks is to compensate for constructing a linearized model so as to minimize the output error caused by nonlinearities in the control system. The neural networks use the backpropagation algorithm for the learning process. The role of simple adaptive controller is to perform the model matching for the linear system with unknown structures to a given linear reference model. In this method, only part of the control input is fed to the PFC. Thus, the proposed method will reduce the offset error, and both of the augmented plant output and the real plant output can follow significantly close to the output of the reference model. Finally, the effectiveness of this method is confirmed through computer simulations.