The article addresses a Mobile Edge Computing (MEC) network with a focus on wireless power transfer technology. It considers a MEC system with multiple end-users and a single edge server based on energy harvesting techniques. The study formulates the Weighted Time Minimization Problem within the MEC system, and it transforms this problem into two sub-problems: power optimization for offloading users and bit optimization for offloading users. In the first phase, given the task bits for a specific user, the convex approximation of the problem is obtained by introducing an upper bound, The Lagrangian method is employed to derive the closed-form solution for the user’s transmission power, and the optimal solution for the transmission rate is obtained through sub-gradient iteration methods.In the second phase, the optimization of offloading users bits is addressed. The optimal offloading bits for users are obtained by using the Alternating Direction Method of Multipliers (ADMM). Simulation experiments (ADMM).Simulation experiments show that the proposed algorithm can effectively reduce system latency.