The installed capacity of photovoltaic power generation occupies an increasing proportion in the power system, and its stability is greatly affected by the fluctuation of solar radiation. Accurate prediction of solar radiation is an important prerequisite for ensuring power grid security and electricity market transactions. The current mainstream solar radiation prediction method is the deep learning method, and the structure design and data selection of the deep learning method determine the prediction accuracy and speed of the network. In this paper, we propose a novel long short-term memory (LSTM) model based on the attention mechanism and genetic algorithm (AGA-LSTM). The attention mechanism is used to assign different weights to each feature, so that the model can focus more attention on the key features. Meanwhile, the structure and data selection parameters of the model are optimized through genetic algorithms, and the time series memory and processing capabilities of LSTM are used to predict the global horizontal irradiance and direct normal irradiance after 5, 10, and 15 min. The proposed AGA-LSTM model was trained and tested with two years of data from the public database Solar Radiation Research Laboratory site of the National Renewable Energy Laboratory. The experimental results show that under the three prediction scales, the prediction performance of the AGA-LSTM model is below 20%, which effectively improves the prediction accuracy compared with the continuous model and some public methods.