This article aims to establish an appointed-time observer-based framework to efficiently address the resilient consensus control problem of linear multiagent systems with malicious attacks. The local appointed-time state observer is skillfully designed for each agent to estimate the agent's actual state value at the appointed time, even in the presence of unknown malicious attacks. Based on the state estimation, a new kind of resilient control strategy is proposed, where a virtual system is constructed for each agent to generate an ideal state value such that the consensus of normal agents can be achieved with the exchange of ideal state values among neighboring agents. To specify the consensus trajectory while achieving resilient consensus, the leader-follower resilient consensus is further studied, where the leader is assumed to be a trusted agent with a bounded control input. Compared with the existing results on the resilient consensus, the proposed distributed resilient controller design reduces the requirement on communication connectivity significantly, where the allowable communication graph is only assumed to contain a directed spanning tree. To verify the theoretical analysis, numerical simulations are finally provided.