When simulating protein adsorption behavior, decisions must first be made regarding how the protein should be oriented on the surface. To address this problem, we have developed a molecular simulation program that combines an empirical adsorption free energy function with an efficient configurational search method to calculate orientation-dependent adsorption free energies between proteins and functionalized surfaces. The configuration space is searched systematically using a quaternion rotation technique, and the adsorption free energy is evaluated using an empirical energy function with an efficient grid-based calculational method. In this paper, the developed method is applied to analyze the preferred orientations of a model protein, lysozyme, on various functionalized alkanethiol self-assembled monolayer (SAM) surfaces by the generation of contour graphs that relate adsorption free energy to adsorbed orientation, and the results are compared with experimental observations. As anticipated, the adsorbed orientation of lysozyme is predicted to be dependent on the discrete organization of the functional groups presented by the surface. Lysozyme, which is a positively charged protein, is predicted to adsorb on its 'side' on both hydrophobic and negatively charged surfaces. On surfaces with discrete positively charged sites, attractive interaction energies can also be obtained due to the presence of discrete local negative charges present on the lysozyme surface. In this case, 'end-on' orientations are preferred. Additionally, SAM surface models with mixed functionality suggest that the interactions between lysozyme and surfaces could be greatly enhanced if individual surface functional groups are able to access the catalytic cleft region of lysozyme, similar to ligand-receptor interactions. The contour graphs generated by this method can be used to identify low-energy orientations that can then be used as starting points for further simulations to investigate conformational changes induced in protein structure following initial adsorption.