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The problem of the leader-follower consensus disturbance rejection under the directed network with fixed topology for a class of multi-agent systems with input delay and exogenous disturbances is discussed. Firstly, for the multi-agent systems with exogenous disturbances, a distributed state observer is given to estimate the state and disturbance simultaneously. Secondly, based on the truncated prediction approach, a consensus protocol is proposed for each agent by utilizing the estimated state and its own disturbance estimate information, which are obtained by using the relative output information between neighbors. Then sufficient conditions for the stability and the observability of the multi-agent systems are constructed by using Lyapunov-Krasovskii theory and the problem of solving feedback gain matrix and observer gain matrix are transformed into calculating linear matrix inequalities (LMIs). Finally, a simulation example is given to demonstrate the feasibility and effectiveness of the results.