The paper presents a novel quantum neural network (QNN) model with variable selection for short term load forecasting. In the proposed QNN model, first, the combiniation of maximum conditonal entropy theory and principal component analysis method is used to select main influential factors with maximum correlation degree to power load index, thus getting effective input variables set. Then the quantum neural network forecating model is constructed. The proposed QNN forecastig model is tested for certain province load data. The experiments and the performance with QNN neural network model are given, and the results showed the method could provide a satisfactory improvement of the forecasting accuracy compared with traditional BP network model.