Privacy-preserving record linkage (PPRL) is the process of linking records from various data sources, ensuring that matching records for the same entity are shared among parties while not disclosing other sensitive data. However, most existing PPRL approaches currently rely on third parties for linking, posing risks of malicious tampering and privacy breaches, making it difficult to ensure the security of the linkage. Therefore, we propose a parallel multi-party PPRL method based on consortium blockchain technology which can effectively address the issue of semi-trusted third-party validation, auditing all parties involved in the PPRL process for potential malicious tampering or attacks. To improve the efficiency and security of consensus within a consortium blockchain, we propose a practical Byzantine fault tolerance consensus algorithm based on matching efficiency. Additionally, we have incorporated homomorphic encryption into Bloom filter encoding to enhance its security. To optimize computational efficiency, we have adopted the MapReduce model for parallel encryption and utilized a binary storage tree as the data structure for similarity computation. The experimental results show that our method can effectively ensure data security while also exhibiting relatively high linkage quality and scalability.