In the era of Internet of Everything, massive connectivity and various demands of latency for Internet of Thing (IoT) devices will be supported by the massive Machine Type Communication (mMTC). Non-Orthogonal Multiple Access (NOMA) and Mobile Edge Computing (MEC) have the advantages of improving network capacity, reducing MTC devices’ (MTCDs) latency and enhancing Quality of Service. Exploiting these benefits, we focus on the energy efficient secure computation offloading in NOMA based mMTC networks for IoT, where the relay equipped with an MEC server and a passive malicious eavesdropper are presented. We optimize the joint computation and communication resource allocation to maximize the secrecy energy efficiency of computation offloading while guaranteeing the delay requirements of MTCDs. Furthermore, we model the subchannels allocation problem as MTCD-to-Subchannel matching. Exploiting difference of convex programming and successive convex approximation, we formulate the Dinkelbach-based SEE optimization algorithm and obtain the closed-form expression of power allocation for MTCDs’ on each subchannel. Based on the communication resources allocation schemes, we propose the Knapsack algorithm to solve the problem of computation resource allocation. Furthermore, we formulate the joint computation and communication resource allocation algorithm for secure computation offloading. Simulation results demonstrate the effectiveness of proposed algorithm for supporting IoT devices energy efficient secure computation offloading.