This paper studies the H consensus problem of multi-agent systems with Lipschitz non-linearities and external disturbances in a general network. The topology is just required to contain a directed spanning tree. Distributed consensus controllers are constructed based on relative states information of neighbour agents. A novel matrix decomposition based approach is introduced to analyse the H consensus problem, in which the H consensus problem is converted into a H control problem of lower dimension system by performing a proper linear variable transformation. Finally, the effectiveness of the theoretical results is illustrated via a numerical simulation.