The offloading method is important when there are multiple mobile nodes and multiple edge servers. In the environment, those mobile nodes connect with edge servers with different bandwidths, thus taking different time and energy for offloading tasks. Considering the system load of edge servers and the attributes (the number of instructions, the size of files, deadlines, and so on) of tasks, the energy-aware offloading problem becomes difficult under our mobile edge environment (MCE). Most of the past work mainly offloads tasks by judging where the job consumes less energy. But sometimes, one task needs more energy because the preferred edge servers have been overloaded. Those methods always do not pay attention to the influence of the scheduling on the future tasks. In this paper, first, we try to execute the job locally when the job costs a lower energy consumption executed on the MD. We suppose that every task is submitted to the mobile server which has the highest bandwidth efficiency. Bandwidth efficiency is defined by the sending ratio, the receiving ratio, and their related power consumption. We sort the task in the descending order of the ratio between the energy consumption executed on the mobile server node and on the MD. Then, we give a "suffrage" definition for the energy consumption executed on different mobile servers for offloading tasks. The task selects the mobile server with the largest suffrage. Simulations show that our method reduces the execution time and the related energy consumption, while keeping a lower value in the number of uncompleted tasks.