This paper considers a full-duplex (FD) mobile-edge computing (MEC) system with non-orthogonal multiple access (NOMA) and energy harvesting (EH), where one group of users simultaneously offload task data to the base station (BS) via NOMA and the BS simultaneously receive data and broadcast energy to other group of users with FD. We aim at minimizing the total energy consumption of the system via power control, time scheduling and computation capacity allocation. To solve this nonconvex problem, we first transform it into an equivalent problem with less variables. The equivalent problem is shown to be convex in each vector with the other two vectors fixed, which allows us to design an iterative algorithm with low complexity. Simulation results show that the proposed algorithm achieves better performance than the conventional methods.