Nowadays, with the advances in wireless communication, the mobile devices are becoming important due to various applications which provide mobile users with plentiful services in the devices. The mobile devices can hardly complete all the computing tasks as they have limitations on the battery capacity, physical size, etc. In order to release these limitations, in the fifth generation (5G), the computing tasks can be offloaded from the mobile devices to the central units (CUs) which are enhanced into edge nodes (ENs) for processing. However, it is still a problem to select the appropriate offloading destination, aiming to improve the load balance for all the ENs. In this paper, we first formulate an optimization problem to improve the load balance of all the ENs for 5G networks in edge computing, considering the time consumption and the privacy conflicts. Then, a load-aware computation offloading method with privacy preservation, named LCOP, is designed. Finally, experimental results and evaluations validate our proposed method is both effective and feasible.