This article addresses the distributed H∞ consensus control problem of general linear multiagent systems with time-varying communication delays and external disturbances. The communication network is subject to arbitrarily bounded and nonuniform time-varying communication delays. Based on the leader-following control mode, a novel distributed state feedback control protocol is proposed to achieve state consensus over undirected fixed topology while guaranteeing a prescribed disturbance rejection objective. By means of Lyapunov analysis and some inequality techniques, admissible upper bounds of nonuniform time-varying delays and H∞ consensus criteria are acquired. As opposed to the existing result for the similar problem, our result has its distinct advantages in that it can accommodate arbitrarily bounded nonuniform time-varying communication delays, and has greater delay margin and better consensus performance. Moreover, the consensus problem for the multiagent systems over connected undirected switching topology is discussed. Finally, a numerical example is provided to show the effectiveness and superiority of these obtained results.