In this article, the convection dominated convection-diffusion problems with the periodic micro-structure are discussed. A two-scale finite element scheme based on the homogenization technique for this kind of problems is provided. The error estimates between the exact solution and the approximation solution of the homogenized equation or the two-scale finite element scheme are analyzed. It is shown that the scheme provided in this article is convergent for any fixed diffusion coefficient δ, and it may be convergent independent of δ under some conditions. The numerical results
demonstrating the theoretical results are presented in this article.