The Navier-Stokes (NS) equations characterize a variety of flows and play an important role in many engineering applications. To describe various problems in fluid dynamics, NS equations need different boundary condition, which is one of the very important factors deciding the behavior of the fluids. So far almost exclusively, the no-slip boundary condition has been considered for motions of fluid in mathematics. However, there exist some flow phenomena, which require the introduction of slip boundary conditions in reality, for instances, blood flow in a vein of an arterial sclerosis patient, or flow of melted iron coming out from a smelting furnace. These phenomena can be modeled by NS equations with a nonlinear slip boundary condition of friction type, which is a variational inequality problem. In this presentation, several discontinuous Galerkin (DG) methods are introduced and analyzed to solve a variational inequality controlled by stationary Stokes equations. Numerical results are reported to demonstrate the theoretical prediction, and show the capability of the DG methods to capture the discontinuity of the problems. In order to solve the problem efficiently, adaptive DG method is designed based on reliable and efficient a residual type posteriori error estimators.