Consensus problems of first-order and second-order multi-agent system with communication delays and input delays are proposed based on the frequency-domain analysis and generalized Nyquist criterion. Supposing that the topology of the multi-agent system is fixed, asymmetrically interconnected digraph and owns a globally reachable node, the sufficient condition for system convergence is obtained. The results show that the condition of convergence is dependent only on system coupling strength, each agent input time delay and the adjacent weights to its neighbors, but independent of communication delay which can affect the dynamics of the system. Finally, simulations are provided to demonstrate the effectiveness of our theoretical results.