A class of n-order resistor network model with external resistor is studied, and an analytical expression for the equivalent resistance between any two nodes is given to solve a resistor network problem. The method used in the research of the article mainly uses the branch current to establish a difference equation model and a boundary condition constraint equation model, and then solves the difference equation system to derive the equivalent resistance analytical formula. At the end of the article, some special case issues are discussed, and the conclusions of the special case are compared and validated with other relevant results. The research work of this article has a good demonstration role for physics educators to carry out practical and innovative research.