Secure deduplication aims to efficiently eliminate redundant data in cloud storage system, where convergent encryption (CE) is widely-used to provide the data confidentiality. As the number of convergent keys (CKs) in CE will increase dramatically with enlarging data, there is a critical issue that how to safely manage the CKs. Previous works usually introduce a fully-trusted key management server (KS) to ensure the CKs security, resulting in data leakage by KS in reality. In this paper, we propose a blockchain-based secure deduplication scheme with reliable CK management, denoted as BDKM, which introduces different secret information to CE to enhance the data confidentiality in different level deduplications. To realize secure and reliable CK management, the CK will be divided into key segments by using secret sharing scheme and distributed on blockchain as transactions. Therefore, only the valid data owner can recover the CK from the blockchain and the original data will be protected even if the adversaries have colluded with cloud service provider. Security analysis and performance evaluation demonstrate that our proposed scheme can remain secure under the proposed security models with a limited overhead.