Abstract: The structure of resistor network model is complex and diverse，which is applied in many fields of natural science.This paper researches a kind of n-step bridge network model，which has not been solved before.The investigations show that the network model contains multiple different network types.In this paper，a simplified equivalent model is adopted and a non-linear difference equation model is established by using Kirchhoff's law to solve this problem.A concise formula of fractional equivalent resistance is obtained and several interesting special conclusions are given，where we explain the reason why this network is called bridge circuit network.

Key words: bridge circuit network, equivalent transform, nonlinear difference equation, Kirchhoff’s laws, equivalent resistance