Structurally modulated graphene presents a new variety of this 2D material which offers a possibility of electronic band engineering and promises to extend a wide range of possible applications of graphene from straintronics, optoelectronics and spintronics, coatings, sensors for batteries, etc. Motivated by these prospects, and a small number of experimental realizations of the modulated graphene systems, we have synthesized and studied epitaxial graphene on stepped Ir(332) substrate. The system was studied with a comprehesive set of experimental techniques which gave the insight into structural characteristics (scanning tunneling microscopy, STM, atomic force microscopy, AFM, and low energy electron diffraction, LEED), electronic band structure (angle-resolved photoemission spectroscopy, ARPES, scanning tunneling spectroscopy, STS, and density functional theory, DFT) and the nature of the inherent strain (polarized Raman spectroscopy). The graphene on Ir(332) caused a severe surface restructuring, consisting of formation of large (111) terraces and (331) step bunches, giving the substrate and graphene a new periodicity. We found that the new periodicity as well as the graphene rotation can be controlled through variation of growth parameters. Furthermore, we found that the ordering of modulated graphene depends on the graphene rotation, which was connected to the size of the moiré unit cell. Measurements of the electronic band structure showed the Dirac cone anisotropy which was attributed to the 1D periodicity present in the system. Additionally, graphene’s local density of states dependent heavily on the specific morphological motifs, which was connected to the measured difference in doping between the graphene on terraces or on step bunches, and to the site specific interaction calculated using DFT. The DFT calculations showed that the graphene binding is strongest on the step edges, which drives the surface restructuring. Furthermore, we have accomplished to transfer graphene from Ir(332) onto SiO2 terminated Si wafer, where the graphene modulation was preserved after the transfer. Such periodically nano-modulated graphene showed inherent presence of uniaxial strain, which is necessary for potential applications.