This paper investigates the consensus problem of general linear discrete-time multi-agent systems by using distributed model predictive control (DMPC) with self-triggered mechanism. First, a novel DMPC based consensus algorithm is proposed, where each agent only needs to obtain its neighbors’ predicted state sequences once at each time step. We prove that the resultant DMPC optimization problem is feasible, and the proposed algorithm guarantees the dynamic consensus of agents. Then, to further reduce the communication cost and the energy consumption of control updates, a self-triggered DMPC based consensus algorithm is proposed with the control input and the triggering interval jointly optimized. Numerical examples including the benchmark problem with platooning vehicles are provided to verify the effectiveness and advantages of the proposed algorithms.