In this paper, arrays of metallic half-ring/rectangle were designed, and their transmission properties were investigated by the finite element method. Fano resonances appeare in the transmission spectra due to the electric field couplings between the half-ring and rectangle. Fano resonant peaks are dependent strongly on the structural parameters and the relative position of the half-ring and rectangle. They are also sensitive to refraction index around the arrays of metallic half-ring/rectangle and the highest sensitivity can be achieved to 862.5 nm/RIU. These results would be helpful for designing the micro-nano photonic devices based on the Fano resonance.