In this study, multiple scale method is introduced for singularly perturbed convection-diffusion equation. In this context, the mentioned problem is transformed into partial differential equation. Besides exponentially fitted difference scheme is established by the method of integral identities with using linear basis functions and interpolating quadrature rules with weight functions and remainder term in integral form. Some numerical experiments have been carried out to validate the theoretical results. The main objective of this article is to compare the multiple scale method and finite difference method for singularly perturbed convection-diffusion problems.