Abstract: We design a consensus protocol based on predictive mechanisms for the second-order discrete-time multi-agent systems and present an equivalent form of the general numerical solution of the model predictive control (MPC) by algebraic theory. A new protocol with equivalent solution without an inverse matrix is beneficial to the theoretical analysis and avoids ahigh computing cost. We also obtain the necessary and sufficient convergence conditions of our proposed protocol and analyze the influence of the protocol parameters on the system's convergence. Simulation results show that the protocol can extend the sampling interval of the discrete-time system, accelerate the convergence rate of the multi-agent systems, and enhance the system's stability.