Congestion of packets in the Internet is the most undesirable problem to securely communicate between end users. Thus, many approaches have been attempting to resolve such a problem. We have already proposed a routing strategy with chaotic neurodynamics. The chaotic neurodynamics is introduced to alleviate the packet congestion, then, the routing strategy shows higher performance for complex networks than the shortest path approach (the Dijkstra algorithm). In this paper, we extend the routing strategy by combining waiting time at adjacent nodes. We show that the improved routing strategy has high performance for the scale-free networks.