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In this paper, we propose a secure computation offloading scheme (SCOS) in intelligently connected vehicle (ICV) networks, aiming to minimize overall latency of computing via offloading part of computational tasks to nearby servers in small cell base stations (SBSs), while securing the information delivered during offloading and feedback phases via physical layer security. Existing computation offloading schemes usually neglected time-varying characteristics of channels and their corresponding secrecy rates, resulting in an inappropriate task partition ratio and a large secrecy outage probability. To address these issues, we utilize an ergodic secrecy rate to determine how many tasks are offloaded to the edge, where ergodic secrecy rate represents the average secrecy rate over all realizations in a time-varying wireless channel. Adaptive wiretap code rates are proposed with a secrecy outage constraint to match time-varying wireless channels. In addition, the proposed secure beamforming and artificial noise (AN) schemes can improve the ergodic secrecy rates of uplink and downlink channels even without eavesdropper channel state information (CSI). Numerical results demonstrate that the proposed schemes have a shorter system delay than the strategies neglecting time-varying characteristics.