In order to solve the constraints of many factors such as ambient temperature, wind speed and solar irradiance on photovoltaic power generation prediction, a long short-term memory （LSTM） neural network model based on similar day analysis and improved whale algorithm optimization to realize short-term prediction of photovoltaic power is proposed. Firstly, the Pearson correlation coefficient is used for feature selection to remove meteorological characteristics that are not correlated with the output power of photovoltaics. Secondly, according to the actual situation that the power generation of photovoltaic power plants is close under similar meteorological conditions, gray relation analysis （GRA） is used to select dates similar to the meteorological characteristics of the forecast day as the training set. Then, an improved whale algorithm（IWOA） is proposed to optimize the hyperparameters of LSTM deep neural network to minimize the root mean square error of the prediction model. Finally, the historical data of photovoltaic power generation of Yulara Desert No.3 photovoltaic power station in Australia is used as experimental data, and the GRA-IWOA-LSTM neural network model is used to make predictions. The simulation results show that the prediction results of the GRA-IWOA-LSTM model are more accurate than the prediction effects of other models under different weather types.