Because of intermittence and fluctuation of photovoltaic (PV) power, it is difficult to enhance prediction accuracy. To sustain high-efficient operation of power system, this paper proposes a hybrid method to predict the short-term PV power. It consists of components separation of PV power, parameters optimization and re-construction of prediction result. Firstly, the methods based on the identifying of feature frequency and mutual information maximum are proposed to optimize the mode number and penalty factor of VMD, respectively. The optimized VMD (OVMD) is used to decompose the complicated fluctuation components of PV power into single component. Then, the improved PSO (IPSO) based on non-linear inertia weight of anti-sine function is proposed to optimize the number of hidden layer nodes, learning rate and iteration number of LSTM network. The optimized LSTM is used to predict each single component of OVMD decomposition. Thirdly, the prediction result of each single component is re-constructed to obtain the final PV prediction power. The experiment result indicates that the prediction accuracy of the proposed method (OVMD-IPSO-LSTM) outperformances the other typical methods. By the improvement of the traditional method (VMD and PSO) and the parameter optimization of LSTM, this hybrid method makes a contribution to the prediction of short-term PV power.