In the present work

an integral equation approach is developed to solve the convection-diffusion equations. In this approach

Green's function of the Laplace equation in the form of series is employed to transform the convection-diffusion equation into an integral equation. With the help of orthogonal polynomials

the integral equation is reduced to an algebraic equation system with a finite number of unknown variables. Finally

this integral equation approach is examined by three examples. The Chebyshev polynomial is used to approximate the one-dimensional convection-diffusion problem with nonhomogeneous boundary conditions and the Fourier series is for the two-dimensional convection-diffusion problem with homogeneous boundary conditions. The comparisons with the finite volume method

finite element method and upwind difference method show that the integral equation approach is more accurate and stable. The stability is also proved by the convection-dominated diffusion problems. Furthermore

it can achieve a satisfactory accuracy even with a small number of grid points.