In this paper, the H∞ consensus control synthesised with transient perfomance for linear muilt-agent systems in directed networks is investigated. Compared with the existing conclusions in undirected networks, the one presented in the article depends less on the structure of the communication topology which is more common. A novel matirx decomposition of Laplacian matrix is introduced, then the consensus problem is converted into an control problem of a lower dimension system via a proper linear variable transformation, which can be analysed by Lyapunov method. A sufficient condition to achive consensus synthesised with transient perfomance is presented. Finally, the effectiveness of the theoretical results is illustrated via a numerical simulation on a two demensional two order UAV model.