Recently, because of the rapid spread of mobile devices, the number of flowing packets in the computer network increases and this causes the congestion of the packets. As one of the effective packet routing methods to remove the packet congestion, a packet routing method using chaotic neurodynamics has already been proposed. By using the chaotic neurodynamics that realizes the decentralized routings of the packets, this method shows higher arrival rate of the packets than the shortest path routing. However, if the number of packets drastically increases, the method shows poor performance because the packets are congested at the hub nodes. We then proposed new routing strategy by chaotic neurodynamics with degree information in this paper. From the results of the numerical simulations, the proposed routing method alleviates the packet congestion at the hub nodes effectively, showing that large number of packets are transmitted to their destinations as compared to the conventional chaotic routing method and the shortest path routing.