This paper investigates the consensus problem for a group of high-order-integrator agents with fixed topology. A linear distributed consensus protocol is proposed, which only depends on the agent's own information and its neighbors' partial information. A necessary and sufficient condition for convergence to consensus is established. It is proved that the topology having a spanning tree is a necessary condition for convergence to consensus. Based on the consensus protocol for networks of high-order-integrator agents, a consensus controller is provided for a group of identical agents with dynamics described by a completely controllable single-input linear time-invariant (LTI) system. It is shown that the consensus of this kind of networks is equivalent to that of networks of high-order-integrator agents. Finally, the parameter design of the protocol is discussed.