This paper proposes a network routing method based on a computational ecology model. The computational ecology model is a mathematical model proposed by Huberman and Hogg, which represents a macro action of multi-agent systems. We formulate routing on a computer network as a resource allocation problem, where packets and links are regarded as agents and resources, respectively. Then, we apply an extended computational ecology model for this problem. Agents conflict so as to get more payoffs from links. As a result, they get the same payoffs, and a good resource allocation is achieved. In each node, each packet selects a link according to the selection rate decided through conflicts, and routing is accomplished autonomously with adaptability on the computer network. Moreover, we improve fault-tolerance of the system by local information exchanges. Finally, we examine the efficiency of the proposed method by computer simulation.