This letter considers a mobile edge computing (MEC) system with one access point (AP) serving multiple users over a multicarrier channel, in the presence of a malicious eavesdropper. In this system, each user can execute the respective computation tasks by partitioning them into two parts, which are computed locally and offloaded to AP, respectively. We exploit the physical-layer security to secure the multiuser computation offloading from being overheard by the eavesdropper. Under this setup, we minimize the weighted sum-energy consumption for these users, subject to the newly imposed secrecy offloading rate constraints and the computation latency constraints, by jointly optimizing their computation and communication resource allocations. We propose an efficient algorithm to solve this problem.