Power forecasting is an important task for achieving energy supply and demand balance and maintaining stable operation of power grids. With the development of distributed offshore photovoltaic systems, the utilization rate of photovoltaic power is constantly improving, while higher requirements are placed on photovoltaic power forecasting. In view of the problems of insufficient sample size, low prediction accuracy, and privacy leakage in the machine learning method for photovoltaic power time series forecasting, this paper proposes a long short-term memory neural network power forecasting model based on federated learning and variational mode decomposition(FL-VMD-LSTM). The meteorological data is preprocessed by principal component analysis and cubic spline interpolation, and the photovoltaic power time series is decomposed into multiple components for stepwise prediction to reduce the non-stationarity and complexity of the photovoltaic power time series. The local training and parameter aggregation method of horizontal federated learning is used to achieve photovoltaic power forecasting under the condition of data privacy security. Four simulation experiments are conducted to verify that the FL-VMD-LSTM model has high accuracy in photovoltaic power forecasting, with RMSE and MAE reduced by 55.7% and 55.5%, respectively, compared with traditional algorithms.