As an innovative distributed ledger technology, a Blockchain has broad application prospects in many industries due to its features of decentralization, traceability, and tamper resistance. However, the existing single-chain structure of Blockchains faces problems such as low concurrency and high latency. The emergence of a new ledger technology based on the directed acyclic graph (DAG) structure is expected to break through the performance bottleneck of traditional Blockchains, but the current consensus mechanism based on the DAG-based Blockchain system is not mature. This study improves the security problems in the open representative voting (ORV), a consensus mechanism of the Nano network for the typical DAG-based Blockchain system, and proposes a consensus mechanism of open election representative voting (OERV) based on the representative election model. The rights and interests of the main representative nodes are dispersed; the degree of decentralization is enhanced, and the network security is improved. The experimental results reveal that the OERV algorithm has high performance and can enhance the stability and security of the system without sacrificing system efficiency. It is of practical significance for promoting the research on the consensus mechanism of DAG-based Blockchains.