Abstract The article aims to explore the heat conduction equation initial boundary value problem of the finite difference method. This paper includes the following two parts of the main content: The first part pared with the traditional heat conduction equation initial boundary value problem of the separation of variables method finite difference method; The second part is the heat conduction equation initial boundary value problem of difference methods for specific examples. Which mainly relates to a method for heat conduction equation initial boundary value problem of the separation of variables method and finite difference method. It first introduces the finite difference method. The basic idea is to use a continuous solution region using finite discrete points constitute a grid to replace, the discrete points are called grid node; the continuous solution of continuous variable function is used in the grid defined on a discrete variables function to approximate; the original equations and boundary conditions of the difference quotient to mercial approximation, integral integral and to approximate, and the differential equations and boundary conditions is ap