Employing the Monte Carlo technique, we study the kinetics of vesicle adsorption at a solid-liquid interface. The proposed model combines a treatment of the surface kinetics, including spontaneous, adsorption- and lipid-membrane-induced decomposition of adsorbed vesicles, and limitations of the adsorption rate by vesicle diffusion in the solution. With this model, we demonstrate different kinetic cases, corresponding to various scenarios of vesicle adsorption and decomposition. The general results are employed to simulate recent experimental kinetic data for adsorption of small phospholipid vesicles at a SiO2 surface.