Abstract: In mobile edge computing, time delay and power consumption are key performance indicators, and they are mutually restricted. This paper studies the joint optimization of time delay and power consumption by distributing tasks between edge and terminal. Firstly, the 0-1 integer programming model for joint optimization of energy consumption and time delay is established on the basis of describing the research problem. Secondly, a branch and bound algorithm for task assignment is designed. Finally, the simulation show that the proposed method can effectively reduce the energy consumption and time delay of mobile edge computing.