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In this paper, we study a mobile edge computing (MEC) network based on non-orthogonal multiple access (NOMA) scheme, in which a user can offload its tasks to two MEC servers through downlink NOMA. Due to security constraint, the confidential tasks must be computed on the trusted server, the remain tasks can be offloaded to other server if needed. In this scenario, we propose a novel secure protocol, namely APS-NOMA MEC, based on access point selection (APS) scheme to guarantee the security constraint. The exact closed-form expression of successful computation probability for this proposed system protocol is derived. We further study the impact of the network parameters on the system performance to confirm the effectiveness of deployment of NOMA in MEC network. The numerical results show that our proposed protocol outperforms the conventional NOMA MEC scheme in terms of …