Surface wrinkles have emerged as a promising avenue for the development of smart adhesives with dynamically tunable adhesion, finding applications in diverse fields, such as soft robots and medical devices. Despite intensive studies and great achievements, it is still challenging to model and simulate the tunable adhesion with surface wrinkles due to roughened surface topologies and pre-stress inside the materials. The lack of a mechanistic understanding hinders the rational design of these smart adhesives. Here, we integrate a lattice model for nonlinear deformations of solids and nonlocal interaction potentials for adhesion in the framework of molecular dynamics to explore the roles of surface wrinkles on adhesion behaviors. We validate the proposed model by comparing wrinkles in a neo-Hookean bilayer with benchmarked results and reproducing the analytical solution for cylindrical adhesion. We then systematically study the pull-off force of the wrinkled surface with varied compressive strains and adhesion energies. Our results reveal the competing effect between the adhesion-induced contact and the roughness due to wrinkles on enhancing or weakening the adhesion. Such understanding provides guidance for tailoring material and geometry as well as loading wrinkled surfaces for different applications.