Aiming at the problem of malicious eavesdropping nodes in the energy limited multi-user Mobile Edge Computing (MEC) system, a joint Wireless Power Transfer (WPT) and MEC secure partial computing offloading programme was proposed. In order to minimize the energy consumption of the system Access Point (AP), the AP energy transmission covariance matrix, local CPU frequency, user unloading bits, user offloading time allocation and user transmission power were jointly optimized under the constraints of computing delay, secure offloading and energy capture. For the AP energy consumption minimization was a non-convex problem, firstly, the original non-convex problem was transformed into a convex problem by Difference of Convex Algorithm (DCA). Then, the optimal solution of the problem was obtained in semi-closed form by Lagrange duality method. When the number of computing tasks is 5 × 105 bits, compared with local computing offloading and secure full computing offloading, the energy consumption of secure partial offloading scheme was reduced by 61.3% and 84.4%, respectively; when the distance between eavesdropping nodes exceeds 25 m, the energy consumed by the secure partial offloading scheme is much less than those of local computing offloading and secure full computing offloading. The simulation results show that the proposed scheme can effectively reduce AP power consumption and enhance system performance gain while ensuring the secure offloading of the physical layer.