<p>This paper discusses the consensus problem of discrete-time multi-agent systems with communication delay under an event-triggered control protocol. To reduce the network communication burden, a dynamic event-triggered mechanism is designed to judge reasonably whether the current system data is necessary to be transmitted. By constructing a threshold parameter based on the measurement error, the designed dynamic event-triggered mechanism can not only maintain a high trigger rate when the system state fluctuates violently but also reduce the trigger rate when the system state fluctuates gently. Compared with the existing event-triggered mechanisms, the number of data transmissions is greatly reduced while the system performance is also ensured under the proposed event-triggered mechanism. In addition, a time-varying communication delay is considered during the data transmission, which is described as dependent on the triggering instants. This model establishes the relationship between the communication delay and the dynamic event-triggered mechanism. Furthermore, Lyapunov functionals with an augmented double summation term are introduced to derive some less conservative criteria. Finally, numerical simulations are conducted to verify the effectiveness of the proposed methods.</p>