An extension of a self-consistent-field lattice theory is developed to study the adsorption of polymers on energetically heterogeneous surfaces. Surface heterogeneity is modeled by introducing distinguishable surface sites which differ in their interaction energy with polymer segments and solvent molecules. The probability for the polymer segments to meet a given kind of site depends on the distribution of the surface sites. In this paper, the adsorption behavior of polymers on a surface with adsorbing and nonadsorbing surface sites is studied. For homopolymers, we find that for high chain length and adsorption energy the adsorbed amount is higher on a surface with a random distribution of adsorbing surface sites as compared to a surface with a patchwise distribution, i.e., where equal surface sites are grouped together. Block copolymers can segregate strongly on a patchwise distributed surface.