In this paper, a distributed event-triggered formation control algorithm for a multi-agent system which consists of linear discrete-time agents is proposed based on control theory. For agents to achieve a formation, it is necessary to communicate with each other to feedback their information. For communication, wireless communications are desirable for various tasks since wired networks can constrain their movement. Also, each agent have to observe their states from sensors. Those energy consumption due to unnecessary calculation and communication of agents may shorten battery life of agents. By using the event-triggered protocol, which updates the control input aperiodically only when certain triggering condition is satisfied, we aim to reduce those calculation and communication by reducing the input update frequency. Also the multi-agent system is guaranteed to achieve a formation by determining the triggering condition of the control input based on Lyapunov’s stability theorem. At the end of the paper, the effectiveness of the proposed algorithm is verified by numerical simulation.