This paper investigates the consensus problem of general linear multi-agent systems under the framework of optimization. A novel distributed receding horizon control (RHC) strategy for consensus is proposed. We show that the consensus protocol generated by the unconstrained distributed RHC can be expressed in an explicit form. Based on the resulting consensus protocol the necessary and sufficient conditions for ensuring consensus are developed. Furthermore, we specify more detailed consensus conditions for multi-agent systems with general and one-dimensional linear dynamics depending on Riccati difference equations (RDEs), respectively. Finally, a case study verifies the proposed scheme and the corresponding theoretical results. (C) 2015 Elsevier Ltd. All rights reserved.