Abstract—In this study, discrete-time high-order linear dynamics of multi-agent systems (MASs) is considered. A distributed minimal-time deadbeat consensus prediction(MDCP) algorithm is proposed that allows each agent to calculate the consensus value of an MAS merely by using the shortest intermittent information series of its own and its neighbors. The challenge of MDCP lies in revealing the relationship between the consensus item of state Z-transform and the annihilating polynomial of matrix pair with intermittent information. Sufficient conditions are derived to guarantee the feasibility of the present MDCP. Finally, both the effectiveness and superiority of the proposed MDCP are substantiated by numerical simulations.