A novel self-recurrent wavelet neural network(SRWNN) super-twisting non-singular fast terminal sliding mode (SRWNN_STNFTSM) control method with prescribed performance is proposed to improve the tracking control performance of ball and plate system in the presence of dynamic uncertainties and unknown perturbations. The prescribed performance function (PPF) is used to convert the originally constrained position error of the ball and plate system into an unconstrained error model. The NFTSMC sliding mode surface is introduced to eliminate the singular problem of conventional terminal sliding mode control, and a compensation term of the tanh function is added to improve the NFTSM sliding mode surface to adjust the convergence speed and tracking accuracy of trajectory tracking. Meanwhile the STNFTSM controller is designed in combination with the super-distortion algorithm (STA) to weaken the influence of chattering and lumped disturbance. Aiming at the lumped disturbance of the system, in order to ensure high tracking accuracy, combined with STNFTSM to design an adaptive SRWNN compensator to eliminate disturbances and ensure robustness. Compared with existing conventional sliding mode control, the simulation verifies that SRWNN_STNFTSM has good performance, and can accurately track the ball and plate system under the lumped disturbance.