In the vehicular edge computing (VEC) environment, centralized offloading strategies are usually hard to address the issue of uneven task distribution, leading to overload at certain nodes. However, distributed offloading strategies come with a higher risk of privacy leakage, making it difficult to address both issues simultaneously. To address the challenge, we propose a multi-user distributed collaborative task offloading optimization method with privacy protection. This method comprehensively considers both latency and energy consumption and introduces a privacy evaluation value as part of the reward evaluation. We aim to maximize the weighted sum of offloading performance and privacy evaluation value. To solve this, we introduce the multi-agent deep reinforcement learning algorithm and make discrete improvements to the algorithm, leading to the proposed Multi-Access Cooperative Optimization with Privacy-Protection (MACOP) algorithm. The simulation results show that the performance of the proposed algorithm is improved over existing methods and effectively solves the overload problem at edge nodes.