For the highly nonlinear short-term photovoltaic power problems affected by a variety of factors, a novel modeling method FVS-KELM based on feature vectors selection (FVS) algorithm and kernel extreme learning machine (KELM) is proposed. Firstly, FVS algorithm maps the input data to the high-dimensional feature space through kernel trick, considering the geometric features, selecting the relevant data subset to form the base vector of the subspace. Secondly, the input data is projected onto the feature subspace, and the final prediction model is established by the KELM method, which does not need set the number of the hidden layer nodes, and uses the kernel function representing the unknown nonlinear feature mapping of the hidden layer, so it has good generalization ability. In order to verify the effectiveness of the FVS-KELM modeling method, it is applied to the benchmark photovoltaic power prediction example provided by Global Energy Forecasting Competition 2014 (GEFCOM2014). Under the same condition, the FVS-KELM method is compared with extreme learning machine (ELM), support vector machine (SVM) method etc. The experimental results show that the FVS-KELM method can not only reduce the computational complexity, but also has good prediction accuracy and robustness, and the model has good generalization.