In the Fourier triangular basis neural network model, the calculation of weights based on BP iterative algorithm has a longer training time. To improve this situation, a Fourier neural network circuit design based on direct weight method is proposed in this paper, which can realize the fast calculation of neural network weights in one step. Moreover, the circuit can realize the dynamic fitting of different curves by adjusting the memristors. Some functions are given as examples to verify the accuracy, error and prediction ability of the fitting. The PSPICE simulation results demonstrate that the average accuracy rate achieves 96.21%. Compared with the BP algorithm on MATLAB, the operation speed of this circuit is improved by several orders of magnitude and has better function prediction ability. © 2024 Institute of Electrical Engineers of Japan and Wiley Periodicals LLC.