As the proportion of installed photovoltaic power generation continues to increase, low output under the influence of large-scale weather systems has an increasingly significant influence on the power grid. There is an urgent need to improve photovoltaic power generation forecasting accuracy and reduce the risk of insufficient output in forecast results. To this end, a multi-task neural network model considering low power output risk (LPOMTN) for short-term photovoltaic forecasting is proposed. First, a numerical weather forecast encoder based on multi-scale CNN-Attention is established, which can extract multi-time scale photovoltaic output characteristics. Then a low-output day prediction module based on parallel CNN decoding and a photovoltaic low-output process prediction module based on the clear-sky model and LSTM were established. The latter uses the prediction results of the former as input, and the two modules perform training modeling in a multi-task learning manner to strengthen the model’s sensitivity to low-output states and improve the accuracy of low-output process predictions. The calculation example results show that LPOMTN has higher average forecasting accuracy for power output processes compared to methods such as XGBoost.