We present a coarse-grained lattice model for (nonionic) surfactant adsorption, which is solved by performing simulations using the Monte Carlo method. We focus our attention on the behavior of surfactant molecules whose head groups have a relatively weak attractive interaction with a solid (hydrophilic) surface. The simulations show that the surfactant molecules start to self-assemble on such a surface at a solution concentration which lies below the cmc. The surfactant forms discrete aggregates on the surface, which are very similar to the almost spherical micellar aggregates in solution, Increasing the surfacant concentration leads to a strong increase of the adsorbed amount. These findings agree well with a wide variety of experimental data for nonionic surfactant molecules adsorbing onto hydrophilic surfaces such as SiO2. We have also studied the effect of the adsorption energy and the head/tail ratio on the adsorption behavior. When the attraction between the surfactant head group and the surface increases, the shape of the adsorbed aggregates changes to a prolatelike structure, and the aggregates orient themselves parallel to the surface, A reduction of the head group size leads to the formation of larger aggregates. The main contribution of this paper lies in the attempt to understand the basic features of a rather broad range of surfactant systems from a simple model which (hopefully) contains the essential characteristics that dominate the adsorption behavior of nonionic surfactants.