In this paper, an Unmanned Aerial Vehicle (UAV) enabled Mobile Edge Computing (MEC) system is studied, in which UAV acts as server to offer computing offloading service to the Mobile Users (MUs) with limited computing capability and energy budget. We aim to minimize the total energy consumption of MUs by jointly optimizing the bit allocation for uplink, computing at the UAV and downlink, along with the UAV trajectory in a unified framework. To this end, a trajectory constraint model is employed to avoid sudden changes of velocity and acceleration during flying. Due to high-order information in use, we lead to a more reasonable nonconvex optimization problem than prior arts. An Alternating Direction Method of Multipliers (ADMM) method is introduced to solve the optimization problem, which is decomposed into a set of easy sub-problems, to meet the requirement on the efficiency in edge computing. Numerical results demon-strate that our approach leads a smoother UAV trajectory, significantly save the energy consump-tion for UAV during flying.