The information exchanged over the smart grid networks is sensitive and private. As such, proper mechanisms must be put in place to protect these messages from security and privacy violations. Although many schemes have been presented in literature to address these challenges, a number of them rarely consider concurrent authentication of smart meters, while some are inefficient or still lack some of the smart grid network security and privacy requirements. In this article, a novel concurrent smart meters authentication algorithm is presented, based on some trusted authority. Formal security analysis of this algorithm is executed using Burrows‐Abadi‐Needham logic, which shows that this algorithm provides strong authentication among the smart meter, utility service provider and trusted authority. In addition, session keys are independently computed and verified between the smart meter and utility service provider with the help of the trusted authority. Informal security analysis shows that this algorithm provides device anonymity, perfect forward key secrecy, strong mutual authentication and is resilient against replay, de‐synchronization, privileged insider, impersonation, eavesdropping, side‐channel, and traceability attacks. In terms of performance, the proposed algorithm exhibits the least communication and computation overheads when compared with other related schemes.