Advanced Metering Infrastructure (AMI) is composed of systems and networks to incorporate changes for modernizing the electricity grid, reduce peak loads, and meet energy efficiency targets. AMI is a privileged target for security attacks with potentially great damage against infrastructures and privacy. For this reason, Key Management has been identified as one of the most challenging topics in AMI development. In this paper, we propose a new Scalable multi-group key management for AMI (SAMI) to secure data communications in an Advanced Metering Infrastructure. It is a key management scheme that can support unicast, multicast and broadcast communications based on an efficient multi-group key graph technique. An analysis of security and performance, and a comparison of our scheme with recently proposed schemes show that our solution induces low storage overhead (reduction reaches 83%) and low communication overhead (reduction reaches 99%) compared to existing solutions.