Power prediction is an important task to achieve the balance of power supply and demand and maintain the stable operation of the power grid. With the development of distributed offshore photovoltaic systems, the utilization rate of photovoltaic is constantly increasing, and higher requirements are put forward for photovoltaic power prediction. In view of the problems such as insufficient sample number, low prediction accuracy and privacy disclosure existing in the photovoltaic power time series prediction by machine learning methods, In this paper, a long-short-term memory neural network power prediction model (FL-VMD-LSTM) based on federated learning and variational mode decomposition is proposed. Principal component analysis (PCA) and cubic spline interpolation are used to preprocess meteorological data. Meanwhile, VMD is used to decompose photovoltaic power time series into multiple components for step-by-step prediction. By reducing the non-stationary and complexity of PV power time series, local training and parameter aggregation methods of horizontal federated learning are used to achieve PV power prediction under the condition of ensuring data privacy and security. Simulation experiments are carried out through four examples, and the verification results show that the FL-VMD-LSTM model has high accuracy in PV power prediction, and the RMSE and MAE are reduced by 55.7% and 55.5%, respectively, compared with the traditional algorithm.