The routing algorithm of SPF (Shortest Path First)  is widely distributed in large scale network such as internet. Since this routing algorithm is designed in order to improve throughput of each packet which is sequentially generated at the nodes, it is not suitable for averaging load balance in the network. The enzymic feedback in the cell is the typical and basic control mechanism which can realize homeostasis of the value of every reactant in the metabolic pathway. The purpose of this study is to design an adaptive routing in which the packets generated at the nodes can be sent to the final destinations with avoiding the partial and time-variant congestions in the network, and the load balance in the network can be averaged. We have proposed here a new biologically inspired adaptive routing algorithm by introducing an enzymic feedback control mechanism in the cell.