Consensus seeking problems are investigated for linear multi-agent systems in this paper. Two kinds of state observers, the decentralized Luenberger observer and the distributed pinning networked observer, are proposed to estimate the group agents’ state. Then, based on the observed state information, a novel distributed hybrid output feedback protocol is proposed. Using an eigenvalue analysis method, necessary and sufficient criteria have been established such that asymptomatic consensus can be achieved for a linear multi-agent system under a fixed directed communication topology. Furthermore, two multi-step algorithms are provided to determine the observer gains and the feedback gains for the proposed observer and distributed hybrid protocol. Finally, a numerical example is given to demonstrate the applicability and efficiency of the proposed consensus protocol.