Due to lack of data or the complex statistical characteristics, it is difficult to ascertain the probability distribution of new energy and various loads when making dispatch decisions. A day-ahead optimal dispatch method of power system considering source and load interval uncertainties is proposed. Firstly, the interval number models of wind power, photovoltaic and various loads are established based on the prediction error. Secondly, taking the daily comprehensive operating cost as the objective function, and considering the constraints of generators, energy storage, and positive and negative backup, a mathematical model of interval optimal dispatch is constructed. Then, by applying interval optimization theory, the interval optimization problem is transformed into a deterministic problem under a certain interval possibility to solve, and the interval optimization dispatch scheme is obtained. Finally, the proposed method is applied in the modified IEEE 10-generator and 39-bus system to validate its effectiveness. The results show that the proposed method is flexible in decision-making. By adjusting the interval possibility degree, the economy and security of the dispatch scheme can be well balanced, and the amount of calculation is small. It is especially suitable for solving the optimal dispatch problem that only grasps the variation range of variables.