For a surfactant-inorganic-water system, we study systemically the epitaxy process of the surfactant-templated inorganic nanomaterial on a patterned surface with a lattice Monte Carlo method. It is found that by using ring-patterned substrate as a template, vertically oriented inorganic material may be formed through the nanometer-scale epitaxy. For all the cases studied in this work, a hemicylinder initially formed on the ring pattern behaves as nucleation sites for the following growth process. Different parameters, such as surfactant architecture, bulk surfactant concentration, fraction of inorganic component, and pattern size, are found to affect the epitaxial growth process of the inorganic nanomaterial. The change of surfactant architecture alters the structure of formed aggregates significantly, thus affecting the epitaxial growth. For the effects of surfactant concentration, it is found that there exists a critical value. If and only if the bulk surfactant concentration is higher than the critical value is the epitaxial growth of inorganic material nucleated from the patterned substrate possible. For the effects of the fraction of the inorganic component, simulation results indicate that there also exists a volume fraction above which the nanomaterial growth is dominated by macrophase separation but not templated by the substrate pattern. The geometry of the chemical modification of the surface also shows significant effects on the nanometer-scale epitaxy, depending on whether its sizes are commensurate with the morphology of the formed inorganic nanomaterials or not.