With the rapid popularization and development of renewable energy, solar photovoltaic power generation systems have become an important energy choice. Convolutional neural network (CNN) models have been widely used in photovoltaic power forecasting, with research focused on problems such as long training times, forecasting accuracy and insufficient speed, etc. Using the advantages of swarm intelligence algorithms such as global optimization, strong adaptability and fast convergence, the improved Aquila optimization algorithm (AO) is used to optimize the structure of neural networks, and the optimal solution is chosen as the structure of neural networks used for subsequent prediction. However, its performance in processing sequence data with time characteristics is not good, so this paper introduces a Long Short-Term Memory (LSTM) neural network which has obvious advantages in time-series analysis. The Cauchy variational strategy is used to improve the model, and then the improved Aquila optimization algorithm (IAO) is used to optimize the parameters of the LSTM neural network to establish a model for predicting the actual photovoltaic power. The experimental results show that the proposed IAO-LSTM photovoltaic power prediction model has less error, and its overall quality and performance are significantly improved compared with the previously proposed AO-CNN model.