A two-dimensional diffusion equation is solved by using the finite Fourier transformation. Through applying the Fourier transformation, a one-dimensional Fredholm-type integral equation of the first kind is derived for the flux and its derivative at the boundary. By solving this equation with given boundary conditions, all of the boundary values are determined. The fluxes inside a region are also obtained by solving similar integral equations. The method of this paper differs from the usual Fourier transformation method in that the solutions are obtained without performing the inverse Fourier transforms. Numerical calculations show that the present method gives higher accuracy with less computation time than the usual finite difference method.