We design a new blockchain-based access control protocol in IoT-enabled smart-grid system, called DBACP-IoTSG. Through the proposed DBACP-IoTSG, the data is securely brought to the service providers from their respective smart meters (SMs). The peer-to-peer (P2P) network is formed by the participating service providers, where the peer nodes are responsible for creating the blocks from the gathered data securely from their corresponding SMs and adding them into the blockchain after validation of the blocks using the voting-based consensus algorithm. In our work, the blockchain is considered as private because the data collected from the consumers of the SMs are private and confidential. By the formal security analysis under the random oracle model, nonmathematical security analysis and software-based formal security verification, DBACP-IoTSG is shown to be resistant against various attacks. We carry out the experimental results of various cryptographic primitives that are needed for comparative analysis using the widely used multiprecision integer and rational arithmetic cryptographic library (MIRACL). A detailed comparative study reveals that DBACP-IoTSG supports more functionality features and provides better security apart from its low communication and computation costs as compared to recently proposed relevant schemes. In addition, the blockchain implementation of DBACP-IoTSG has been performed to measure computational time needed for the varied number of blocks addition and also the varied number of transactions per block in the blockchain.