Mobile edge computing (MEC) integrated with radio frequency-based wireless power transfer (WPT) has became a promising trend to shorten task delay and achieve sustainable operations of computing system, as it continuously provides energy to wireless devices (WDs) and allows computation tasks offloading to a powerful edge server nearby. Furthermore, introducing the relay technique to WPT-MEC system could improve offloading capability and energy efficiency, especially when the condition of the wireless channels between server and WDs is poor. In this paper, we seek to maximize the energy efficiency (EE) for a multi-user relay-aided MEC network powered by WPT, where binary offloading policy is followed in WDs and partial offloading policy is adopted in the relay. We aim to jointly optimize the relay’s computing configurations, wireless charge time fraction and WDs offloading strategy, that faces great challenge due to the strong coupling of multi-user computing mode selection and hybrid offloading model among WDs and relay. To tackle the problem, we formulated it as a mixed integer nonlinear programming (MINLP) problem and design an iterative algorithm based on Dinkelbach’s method and alternating direction method of multipliers (ADMM) decomposition technique to solve it. We first transform the original fractional programming problem into a more tractable problem in a subtraction form based on Dinkelbach’s method. Then according to ADMM technique, we decompose the multi-user offloading problem into multiple subproblems which can be solved in a distributed model. For an iterative calculating step, we propose a Bi-Search algorithm for CPU frequency and transmission power optimization and a DAI-Based algorithm to choose the time fraction of wireless power charging. The simulation results show that our proposed algorithm convergence fast and derive a 15% higher energy efficiency than other benchmark methods.