Photovoltaic (PV) power generation has strong uncertainty and volatility due to weather conditions, which reduces the accuracy of short-term PV power generation forecasting and hinders the efficient operation of the power grid. To reduce the impact of weather on the accuracy of short-term PV power generation forecasting, this paper proposes a method of combining support vector machine (SVM) and particle swarm optimization (PSO)-optimized backpropagation (BP) neural network for short-term PV power generation forecasting. Firstly, we use the SVM kernel function classification method to classify weather into three categories: sunny, cloudy, and rainy, and train the neural network model after classification with PV power generation data under the three weather types. Then, in order to further improve the prediction accuracy, the PSO algorithm is used to optimize the initial parameters and learning rate of the BP neural network, and optimized PSO-BP neural network is applied to perform short-term forecasting on the SVM classified PV power generation data. Simulation results show that the proposed method (SVM-PSO-BP) can significantly improve the accuracy of short-term PV power generation forecasting.