With the ongoing revolutionary growth of the industrial Internet of Things and smart grid networks, smart grid (SG) communication has been acknowledged as a next-generation network for intelligent and efficient electric power transmission. In SG networks, smart meters (SMs) generally send requests for electricity demand to service providers (SPs), which deal with the requests for efficient energy distribution. However, SGs experience many security issues with the deployed SMs and untrusted wireless communication. To tackle these security issues, we propose a privacy-preserving authentication scheme for demand response management in SGs, called BPPS. It can resist various attacks and achieve secure mutual authentication with key agreement; moreover, it provides integrity of demand-response data using blockchain. Moreover, we perform the informal and formal (mathematical) security analysis to confirm that BPPS is secure against various attacks and achieves session key security, respectively. Furthermore, we conduct the performance and simulation analysis for SGs using NS3 and Ethereum testnet. Consequently, BPPS provides high-level security and can be applied to actual SG networks.