Here, we report the fabrication of a graphene-based Bragg grating (one-dimensional photonic crystal) and experimentally demonstrate the excitation of surface electromagnetic waves in the periodic structure using prism coupling technique. Surface electromagnetic waves are non-radiative electromagnetic modes that appear on the surface of semi-infinite 1D photonic crystal. In order to fabricate the graphene-based Bragg grating, alternating layers of high (graphene) and low (PMMA) refractive index materials have been used. The reflectivity plot shows a deepest, narrow dip after total internal reflection angle corresponds to the surface electromagnetic mode propagating at the Bragg grating/air boundary. The proposed graphene based Bragg grating can find a variety of potential surface electromagnetic wave applications such as sensors, fluorescence emission enhancement, modulators, etc.