In this study, the given-time H consensus problem over networks with directed information flow and Markov jump topologies is addressed. Our focus is on keeping the disagreement dynamics of networks confined within the prescribed bound in the fixed time interval. Compared with the asymptotical consensus in infinite settling time, the proposed algorithm is less conservative. In addition, a new model transformation approach is presented to make the design results more advantageous in commonality. Simulation results show the effectiveness of the proposed controller, and reveal that the prescribed boundary of the disagreement trajectory has an effect on disturbance rejection performance.