In this study, the adhesive contact problem for a functionally graded coating with exponentially varying modulus is investigated. The MD model is used to describe the adhesion effect between a rigid cylindrical indenter and a functionally graded coated half-space. The method of Fourier integral transform is applied to convert the controlling equation of the two-dimensional adhesive contact problem to the singular integral equations with Cauchy kernel. The numerical calculation is conducted to achieve the effects of the adhesion parameter and the stiffness ratio on the pull-out force, indentation, contact stresses and adhesion region. The results provide a way to improve the performance of coating on contact phenomena.