Deep learning model has been widely used in time series prediction. However, the traditional deep learning point prediction model pays more attention to the predicted value at a certain moment in the future, and cannot describe the uncertainty of complex time series prediction. In addition, the prediction process of most deep learning models is opaque, and users lack understanding of the internal mechanism of deep learning prediction models. As a result, the interpretability of the model prediction is low. To tackle the above issues, this paper carries out the following two aspects of research: Firstly, quantile regression theory is introduced to describe the uncertainty characteristics of complex time series prediction; Secondly, an interpretable deep learning model is constructed and applied to power load prediction in a region of New York State. The results show that the prediction model in this paper has good interval prediction results on the two data sets. The confidence level is 95%, the PICP values of the model in January and July are 94.28% and 93.23%, respectively. The interval coverage tends to the confidence level. Compared with the comparison model, the proposed model has high prediction accuracy and strong generalization ability. It can improve the stability of short-term power load prediction and provide data support for the power grid manager's decision making.