As a next-generation power system, the smart grid can implement fine-grained smart metering data collection to optimize energy utilization. Smart meters face serious security challenges, such as a trusted third party or a trusted authority being attacked, which leads to the disclosure of user privacy. Blockchain provides a viable solution that can use its key technologies to solve this problem. Blockchain is a new type of decentralized protocol that does not require a trusted third party or a central authority. Therefore, this paper proposes a decentralized privacy-preserving data aggregation (DPPDA) scheme for smart grid based on blockchain. In this scheme, the leader election algorithm is used to select a smart meter in the residential area as a mining node to build a block. The node adopts Paillier cryptosystem algorithm to aggregate the user's power consumption data. Boneh-Lynn-Shacham short signature and SHA-256 function are applied to ensure the confidentiality and integrity of user data, which is convenient for billing and power regulation. The scheme protects user privacy data while achieving decentralization, without relying on TTP or CA. Security analysis shows that our scheme meets the security and privacy requirements of smart grid data aggregation. The experimental results show that this scheme is more efficient than existing competing schemes in terms of computation and communication overhead.