For the task offloading problem of minimizing latency in mobile edge computing, a quantum genetic algorithm is proposed to achieve the minimum total latency of computing tasks under energy consumption constraints. Firstly, with the offloading strategy minimizing the total latency as the optimization objective, a system model and a computing model are established; secondly, by balancing the conditions of minimizing total latency with energy consumption and computing resources constraints, a target function for minimizing total latency is constructed; finally, by combining the quantum genetic algorithm with quantum mutation gates and elite retention strategies, an offloading strategy for minimizing total latency is obtained. Simulation experiments show that compared with other offloading strategies, the proposed offloading strategy has a smaller total latency under different energy consumption constraints and different numbers of computing tasks, and its total latency is reduced by 7.3% compared with the genetic algorithm and by 4.3% compared with the adaptive particle swarm optimization algorithm under different task data volumes.