In this study, a MOKE (Magneto-optical Kerr effect) measurement method for magnetic nanostructures is proposed. Theoretically, the MOKE signal enhancement can be predicted and confirmed when an anti-reflection coated substrate is used. Since MOKE is a ratio of reflectivity and the difference between the reflectivities for two magnetic states, when the reflectivity of the substrate part is reduced by employing an anti-reflection coated substrate, MOKE signal enhancement can be achieved. The enhancement is confirmed by simple numerical MOKE calculations. When the reflectivity of an anti-reflection coated substrate is 0.7%, the calculated MOKE signal is about 79% of its bulk values for the 100-nm wide Fe nanowire with a 1500-nm radius laser beam. It was found that, for various numerical calculations, a larger MOKE signal is obtained relative to a smaller substrate reflectivity.