The world is facing an urgent need to provide secure communication and data access control in advanced metering infrastructure (AMI) because conventional cryptographic key management and authentication protocols are at stake. The cryptography schemes entirely rely on trusted third parties (TTPs), leading to a single point of failure and increasing network overhead. In response to this inefficiency and security compromise, this study proposes a blockchain-enabled distributed AMI secure communication scheme. In the proposed work, smart contract (SC), an integrated part of the blockchain, is programmed to substitute traditional TTP-based transaction systems, which operate in a distributed, immutable, and trustworthy manner. In this paper, we implemented practical Byzantine fault tolerance (PBFT) consensus algorithm and Hyperledger Fabric (HLF) blockchain platform to ensure Byzantine fault tolerance in the blockchain transaction. Performance analysis shows that the proposed BC-AMI scheme has the advantage of incurring the least amount of communication and time costs compared with similar studies while ensuring security against some common cyber-attacks.