In view of the growing contradiction between the intensive computation demands and the resource limitations of mobile users, mobile edge computing (MEC) and simultaneous wireless information and power transfer (SWIPT) have emerged as new paradigms towards 5G communication. However, coordinating the communication and computation between users and edge servers proves to be challenging for MEC. In this paper, we propose a novel multiuser full-duplex (FD) communication system that combines MEC and SWIPT technology in order to take the advantage of high-speed mobile computing and long-lasting self-sustainability. Through MEC technology, users are able to calculate local computation tasks using their batteries, and can offload partial computation tasks to the base station (BS) to reduce their energy shortage. Moreover, users can refill their batteries while receiving the computation result sent by the BS, thus benefiting from SWIPT technology. The FD mode can potentially increase the system performance by allowing the simultaneous transmitting and receiving of computation tasks. Our work aims to minimize the energy consumption of the system, while formulating resource allocation as a joint non-linear optimization problem. We decouple the original non-convex problem into two subproblems and solve them using a proposed algorithm that applies group iterative optimization. Numerical results prove that the proposed algorithm is superior to other two comparison schemes and can significantly reduce the system energy consumption and the latency. INDEX TERMS Full-duplex, mobile edge computing, offload, simultaneous wireless information and power transfer, group iterative optimization. FANGNI CHEN received the B.S. degree in communication engineering and the Ph.D. degree in information and communication engineering from Zhejiang University, China, in 2003 and 2008, respectively.