This article studies the problem of leader-following consensus control in one type of networked multi-agent systems (MASs) subject to finite communication rates and suffering from sensor and actuator false data injection (FDI) attacks. We propose a novel distributed control protocol based on event-triggered and adaptive control theory aimed at ensuring the studied MASs can achieve resilient consensus with cooperative uniform ultimate boundedness (UUB). To this end, a distributed estimator is initially designed to enable the follower agents to estimate the leader agent’s state. Subsequently, internal adaptive controllers are devised for each follower agent so as to mitigate the effect of attack signals. Finally, an event-triggered transmission logic is formulated to address scenarios involving finite communication rates. Numerical simulations are finally conducted to validate the efficacy of the proposed control method.