This article addresses the distributed H-infinity consensus problem of multi-agent systems with general linear node dynamics using relative output measurements. The notion of H-infinity consensus performance region is first introduced and then analysed as a basis for the protocol design. A new kind of distributed observer-type H-infinity protocols is further proposed. Theoretical analysis indicates that the distributed H-infinity consensus problem can be solved if and only if the coupling strength of the protocol belongs to the H-infinity performance region of the closed-loop network. Finally, some numerical simulations are provided to illustrate the effectiveness of the theoretical results.