The grid connected power supply system of new energy has high intermittency and uncertainty, which will bring great challenges to the balance of power production and dispatching. How to quantify the uncertainty of power load plays an important role in the safe and economical operation of power system. Therefore, this paper proposes a deep learning interval prediction model based on multi-objective optimization and Bayesian optimization (MOBO), which can describe the variation trend of power load at a given confidence level. In the process of building the prediction model, we calculated the prediction interval of power load at different points according to the quantile regression theory, and then screened the reasonable prediction model through the validity test. At the same time, multi-objective optimization and Bayesian optimization algorithm theory are used to tune the hyperparameters of the deep learning model. In this paper, the power load dataset of Millwood, New York, USA is used to verify the proposed model. The experimental results show that the proposed model has greater prediction interval coverage probability and smaller prediction interval normalized average width at different confidence levels than other models, besides more accurately describes the fluctuation range of future electricity load.