Mobile-edge cloud computing, an emerging and prospective computing paradigm, can facilitate the complex application execution on resource-constrained mobile devices by offloading computation-intensive tasks to the mobile-edge cloud server, which is usually deployed in close proximity to the wireless access point. However, in the multichannel wireless interference environment, the competition of mobile users for communication resources is not conducive to the energy efficiency of task offloading. Therefore, how to make the offloading decision for each mobile user and select its suitable channel become critical issues. In this paper, the problem of the offloading decision is formulated as a 0-1 nonlinear integer programming problem under the constraints of channel interference threshold and the time deadline. Through the classification and priority determination for the mobile devices, a reverse auction-based offloading method is proposed to solve this optimization problem for energy efficiency improvement. The proposed algorithm not only achieves the task offloading decision but also gives the facility of resource allocation. In the energy efficiency performance aspects, simulation results show the superiority of the proposed scheme.