This study focused the short-term problem of predicting the photovoltaic (PV) output power from plants where there are insufficient solar radiation data. To explore this, China's Longyangxia hydro-PV power plant was selected for a case. First, based on the correlation coefficient method, the meteorological elements strongly related to PV output power were selected. Second, the sample set was classified based on different weather types. Third, the weather types and elements were used to establish two neural network short-term prediction models: the stationary BP model with forward propagation, and dynamic Elman model with backward propagation. The selected meteorological elements included sunshine hours, daily maximum temperature, daily minimum temperature, average relative humidity, and minimum relative humidity. The results showed that sunny days were associated with higher prediction accuracy than cloudy days, rainy and snowy days. When comparing the two prediction models, the Elman model was more accurate than the BP model. The study has important reference value for making short-term predictions about PV output power in areas that lack solar radiation data.