With the large capacity of photovoltaic power generation connected to the grid, in order to reduce the randomness of photovoltaic power generation output, a long short-term memory (LSTM) based on an improved moth-flame optimization (IMFO) algorithm is proposed to predict photovoltaic power generation power. Firstly, through data preprocessing, grey relational analysis is conducted to reduce the dimensionality of input variables. Then, based on the selected input variables, similar-day sample selection is performed using the grey relational analysis method. Secondly, the position update formula are improved to enhance the performance of the moth algorithm. Then, the improved moth algorithm is used in the optimization of the number of network layers and learning rate of the LSTM to improve its prediction accuracy and reduce randomness. Finally, based on the pre-processed samples of similar days, the optimized LSTM is adopted for power prediction. Simulation results show that the prediction accuracy of the model has been improved to a certain extent, which meets the actual engineering requirements.