In the electricity market environment, the market clearing price has strong volatility, periodicity and randomness, which makes it more difficult to select the input features of artificial neural network forecasting. Although the traditional back propagation (BP) neural network has been applied early in electricity price forecasting, it has the problem of low forecasting accuracy. For this reason, this paper uses the maximum information coefficient and Pearson correlation analysis to determine the main factors affecting electricity price fluctuation as the input factors of the forecasting model. The improved particle swarm optimization algorithm, called simulated annealing particle swarm optimization (SAPSO), is used to optimize the BP neural network to establish the SAPSO-BP short-term electricity price forecasting model and the actual sample data are used to simulate and calculate. The results show that the SAPSO-BP price forecasting model has a high degree of fit and the average relative error and mean square error of the forecasting model are lower than those of the BP network model and PSO-BP model, as well as better than the PSO-BP model in terms of convergence speed and accuracy, which provides an effective method for improving the accuracy of short-term electricity price forecasting.