The problem of high energy consumption for mobile devices in mobile edge computing is becoming increasingly prominent. In order to reduce the energy consumption of the mobile devices, an Energy-aware computation Offloading for Workflows (EOW) was proposed. Technically, the average waiting time of computing tasks in edge devices was analyzed based on queuing theory, and the time consumption and energy consumption models for mobile devices were established. Then a corresponding computation offloading method, by leveraging NSGA-Ⅲ (Non-dominated Sorting Genetic Algorithm Ⅲ) was designed to offload the computing tasks reasonably. Part computing tasks were processed by the mobile devices, or offloaded to the edge computing platform and the remote cloud, achieving the goal of energy-saving for all the mobile devices. Finally, comparison experiments were conducted on the CloudSim platform. The experimental results show that EOW can effectively reduce the energy consumption of all the mobile devices and satisfy the deadline of all the workflows.