Multi-access edge computing (MEC) has been regarded as a promising technique for enhancing computation capabilities for wireless networks. In this paper, we study physical layer security in an MEC system where multiple users offload partial of their computation tasks to a base station simultaneously based on non-orthogonal multiple access (NOMA), in the presence of a malicious eavesdropper. Secrecy outage probability is adopted to measure the security performance of the computation offloading against eavesdropping attacks. We aim to minimize the sum energy consumption of all the users, subject to constraints in terms of the secrecy offloading rate, the secrecy outage probability, and the decoding order of NOMA. Although the original optimization problem is non-convex and challenging to solve, we put forward an efficient algorithm based on sequential convex approximation and penalty dual decomposition. Numerical results are eventually provided to validate the convergence of the proposed algorithm and its superior energy efficiency with secrecy requirements.