The adsorption of model proteins onto brush-coated surfaces can occur via two modes. Primary adsorption at the surface, where short range attraction is dominant, is important for small proteins and may be repressed by increasing the grafting density. Secondary adsorption, due to van der Waals attraction, occurs at the outer edge of the brush. Large rodlike proteins are likely to adsorb in this fashion. This mode may be repressed by increasing the brush thickness. The thermodynamics and kinetics of adsorption of model proteins are considered within a simple analytical theory distinguishing between the different adsorption mechanisms of small and big proteins.