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The integration of blockchain into parked vehicle edge computing (PVEC) has emerged as a promising approach to mitigate the inherent trust challenges in distributed and untrusted computing environments. However, during task offloading and consensus, vehicles are vulnerable to location information disclosure, leading to privacy leakage. To address this problem, we propose a location differential privacy-enabled blockchain PVEC (DBPVEC) framework to protect location information during offloading and consensus. Specifically, we design a location differential privacy mechanism based on the Laplace mechanism and theoretically prove that it satisfies ε-differential privacy. This mechanism perturbs vehicles’ locations, and a privacy-preserving offloading strategy is designed to enhance the Hotstuff consensus and protect location privacy in edge computing. Subsequently, we formulate a joint optimization problem, considering system energy consumption, latency, and privacy strength. To solve it, we design a two-layer deep reinforcement learning (DRL) algorithm, with a Deep Q-Network (DQN) as the upper layer and a Deep Deterministic Policy Gradient (DDPG) as the lower layer, to determine the optimal offloading strategy. The experimental results demonstrate that our scheme achieves significant reductions compared to the two baseline methods: the total cost decreases by 68.31% and 63.25%, energy consumption by 9.96% and 16.27%, and delay by 31.46% and 18.07%, respectively. Moreover, it effectively preserves vehicle location privacy during task offloading and consensus while maintaining favorable performance in energy consumption and latency.