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This article investigates the partial-form model-free adaptive control (MFAC) issue for a class of discrete-time nonlinear systems. An improved partial-form MFAC design named IPFMFAC-NN is proposed, where neural networks are introduced to enhance the control performance. With the excellent approximation ability of radial basis function (RBF) neural networks, the pseudo gradient (PG) values of control method can be directly approximated online using the measured input and output data of the controlled system. Besides, long short-term memory (LSTM) neural networks are used to tune the essential parameters of the control method online with system error set and gradient information set. Finally, the effectiveness and applicability are verified by SISO discrete nonlinear system simulation and three-tank system simulation, and experimental results demonstrate that the proposed method achieves the best control performance in all five indices. Especially compared with the partial-form MFAC, the proposed method reduces the <inline-formula> <tex-math notation="LaTeX">$RMSE$ </tex-math></inline-formula> index by 43.83&#x0025; and 6.39&#x0025;, respectively in two simulations, making it a promising control method for discrete-time nonlinear systems.