With the aim to solve the leader-following consensus problem for a class of strict-feedback multi-agent systems with unknown disturbances and input saturation under a directed topology, this paper proposes a distributed event-triggered control approach based on disturbance observer. First, this approach designs a disturbance observer to estimate unknown disturbances, and then combining the dynamic surface control with the adaptive backstepping approach, the control input is obtained. Second, a relative threshold event-triggered control strategy is adopted to solve the problem of limited communication resources. Using the saturation compensation system, a mismatch between the controller signal and the actuator signal is compensated. Besides, using the Lyapunov stability theory, it can be proved that all signals of the closed-loop system are semiglobally uniformly ultimately bounded. Finally, simulation is conducted to evaluate the performance of the proposed approach, and the simulation results prove the effectiveness of the proposed control approach.