Internet of Vehicle (IoV) in Mobile Edge Computing (MEC) Environments have significantly enhanced road traffic conditions. The dynamic nature of IoV topology leads to massive data growth, posing challenges in both data processing inefficiencies by vehicular nodes and their limited capacity to support high-overhead encryption methods. Addressing these challenges, a Blockchain-based Secure and Efficient Batch Digital Signature Verification Scheme for Resource-constrained IoV (BDSV) are proposed in this paper. The BDSV scheme verifies the registration information and traffic data generated by vehicles through the collaboration of the road test equipment operator, nodes, and RSUs. It ensures the validation of blockchain consensus and chained index table. Rigorous security proofs demonstrate that BDSV is resilient against attacks, such as man-in-the-middle (MitM) and forward-backward security breaches. Meanwhile, the BDSV scheme incorporates MEC technology, deploying blockchain nodes in MEC nodes, further improving the performance and efficiency of IoV. Experimental results illustrate that BDSV outperforms other algorithms, reducing IoV data transmission delay and signature verification overhead by 17.38 \(\%\) and 19.83 \(\%\) respectively. Moreover, BDSV exhibits superior performance in terms of authentication overhead and throughput, effectively meeting the security, Reliability, and processing speed requirements of Resource-constrained IoV.