There are three common non-homogeneous boundary conditions for the solution of wave equation in one-dimensional finite interval by using the separation of variables. The homogeneity of non-homogeneous boundary conditions often leads to equation non-homogeneous. According to non-homogeneous conditions of the equation and the boundary, introduces appropriate auxiliary functions by judging conditions, and obtained the homogeneous solution method for non-homogeneous boundary conditions and non-homogeneous equation.