Accurate forecasting of photovoltaic (PV) power is essential for power system dispatch and decision-making. To enhance the prediction accuracy of PV power, a data-driven short-term forecasting method based on similar days and a bi-layer correction long short-term memory (LSTM) model is proposed. Firstly, both PV power and related meteorological data are normalized, and key factors influencing PV power are identified using the Pearson correlation coefficient, reducing the dimensions of the training dataset. Nextly, the Fréchet distance algorithm is applied to match similar days with the target prediction day, improving the quality of the training data. Then, based on numerical weather predictions, the initial PV power forecast is obtained through the baseline LSTM using feature learning. A correction LSTM, using a time series approach, predicts the error and adjusts the initial forecast to produce the final prediction. A case study uses real-world data under different weather conditions, i.e., sunny, cloudy, and rainy conditions. It shows that the proposed model consistently delivers accurate short-term PV power predictions for the next 24 hours. The model significantly improves accuracy compared to existing methods.