We study the equivalent resistance of an n - step network with tripod structure，which is a profound problem，has not been resolved before. The network model contains seven arbitrary parameters which make the network contain a number of different types. First of all，we establish a nonlinear difference equation by means of simplifying a complex graphics into a simple equivalent model; next，we construct the method of equivalent transformation to obtain the general solution of the nonlinear difference equation. Finally，we create a new concept of negative resistance for the needs of the equivalent conversion，and obtain two general resistance formulae of an n - step network with tripod structure. We compare several results by making use of a number of specific examples in 　　the special conditions. Our method and the results are suitable for the research of complex impedance network as well.