The Internet of connected vehicles (IoV) is employed to collect real-time traffic conditions for transportation control systems, and the computing tasks are available to be offloaded from the vehicles to the edge computing devices (ECDs) for implementation. Despite numerous benefits of IoV and ECDs, the wireless communication for computation offloading increases the risk of privacy leakage, which may consequently lead to tracking, identity tampering and virtual vehicle hijacking. Therefore, it remains a challenge to avoid privacy conflicts for computation offloading to the ECDs in IoV. To address this challenge, an edge computing-enabled computation offloading method, named ECO, with privacy preservation for IoV is proposed in this paper. Technically, the privacy conflicts of the computing tasks in IoV are analyzed in a formalized way. Then, vehicle-to-vehicle (V2V) communication-based routing for a vehicle is designed to acquire the routing vehicles from the origin vehicle where the computing task is located at the destination vehicle. NSGA-II (non-dominated sorting genetic algorithm II) is adopted to realize multi-objective optimization to reduce the execution time and energy consumption of ECDs and prevent privacy conflicts of the computing tasks. Finally, experimental evaluations are conducted to validate the efficiency and effectiveness of ECO.