With the emergence of low-latency applications such as driverless cars, online gaming, and virtual reality, it is becoming increasingly difficult to meet users’ demands for service quality using the traditional centralized mobile cloud computing model. In order to make up for the shortages of cloud computing, mobile edge computing came into being, which provides users with computing and storage resources by migrating computing tasks to network edge servers through computation offloading. However, most of the existing work processes only consider single-objective performance optimization of delay or energy consumption, and do not consider the balanced optimization of delay and energy consumption. Therefore, in order to reduce task delay and equipment energy consumption, a multi-user joint computation offloading and resource allocation strategy is proposed. In this strategy, the Lagrange multiplier method is used to obtain the optimal allocation of computing resources for a given offloading decision. Then, a computation offloading algorithm based on a greedy algorithm is proposed to obtain the optimal offloading decision; the final solution is obtained through continuous iteration. Experimental results show that, compared with the benchmark algorithm, the proposed algorithm can reduce system costs by up to 40%.