The intermittent nature of photovoltaic (PV) power poses significant challenges to grid operations. However, accurate forecasting is difficult since PV power depends on weather conditions that fluctuate within minutes. To address this, a novel multi-layer weather classification-based regression model (MWCR) is developed to predict the PV output power for the coming 24 h in different datasets with 1-h and 5-min as time steps. The key idea is to classify weather conditions at each time step to capture the rapid PV power fluctuations. To address the absence of irradiance sensors, the power ratio of predicted power obtained by a long-short term memory (LSTM) model over the maximum power in a clear sky is used to reflect sky condition. Classification is based on power ratio, local irradiance, temperature, wind speed, and humidity. Then, for each class, a regression model with the same inputs is developed. To improve the accuracy of the model, an LSTM model predicting power is integrated as an additional input to the regression model. Prediction results of three datasets at 1-h and 5-min time steps demonstrate superior accuracy for both models compared to an LSTM model alone in all testing datasets, especially on a day with high PV power fluctuations.