A perturbational h4 compact exponential finite difference scheme with diagonally dominant coefficient matrix and upwind effect is developed for the convective diffusion equation. Perturbations of second order arerted on the convective coefficients and source term of an h2 exponential finite difference scheme proposed in this paper based on a transtormation to eliminate the upwind effect of the convective diffusion equation. Four numerical examples including one to three-dimensional model equations of fluid flow and a problem of natural convective heat transfer are given to illustrate the excellent behavior of the present exponential schemes. Besides, the h4 accuracy of the perturbational scheme is vernfied using double precision arithmetic.