Due to intelligent electronic management, the smart grid has recently played a significant role in modern energy infrastructure. However, along with widespread deployment of the smart grid, many potential security threats (e.g., impersonation attack, replay attack, man-in-the-middle attack) rise to the surface. To defend against these possible attacks, numerous cryptography-based authentication schemes have been proposed for the smart grid. Most of the schemes investigate the secret key distribution problem, but the re-quirement of decentralized registration authority is neglected. In addition, over-complicated cryptographic primitives also strengthen the burden of authentication system. In contrast with previous researches, our proposed BlockSLAP utilizes cutting-edge blockchain technology as well as smart contract to decentralize the registration authority and reduce the interaction process to 2 steps. Moreover, our protocol is proved secure under computational hard assumption and informal security analysis. Finally, experimental results show that smart grid authentication performance in our protocol has been improved compared to the other existing ECC-related schemes.