In this paper, we propose two kinds of composite structures based on the one- and two-dimensional (1D&2D) gold grating on a gold film for plasmonic refractive index sensing. The resonance modes and sensing characteristics of the composite structures are numerically simulated by the finite-difference time-domain method. The composite structure of the 1D gold semi-cylinder grating and gold film is analyzed first, and the optimized parameters of the grating period are obtained. The sensitivity and figure of merit (FOM) can reach 660RIU/nm and 169RIU⁻¹, respectively. Then, we replace the 1D grating with the 2D gold semi-sphere particles array and find that the 2D grating composite structure can excite strong surface plasmon resonance intensity in a wider period range. The sensitivity and FOM of the improved composite structure can reach 985 RIU/nm and 298 RIU⁻¹, respectively. At last, the comparison results of the sensing performance of the two structures are discussed. The proposed structures can be used for bio-chemical refractive index sensing.