Considering the equivalent resistance between any two nodes of n step resistor network，which is a difficult problem that has not been solved before.First of all，we present a general formula of equivalent resistance between any two nodes of n step resistor network. Second，we model the differential equation by the method of network analysis，and model the constraint equation by the currents of input and output，thus the formula of equivalent resistance is proved by using the above equations.Finally，the formula of equivalent resistance of infinite network is given，and the conclusions in special cases are compared and discussed with other conclusions，and thus the correctness of the conclusions obtained is validated.