Using three-dimensional (3D) finite-difference time-domain method, optical and sensing properties of local surface plasmon resonances of triangle metal nanoparticles with different geometric parameters are studied numerically. The influences of four parameters, including the height, the tip angle, the radius of curvature of vertex angle of the triangle and the gap, on the extinction spectra, bulk refractive index sensitivities and figures of merit of single-triangle and bi-triangle gold nanostructures are analyzed in detail. An optimization method of sensing properties is given based on the results of numerical calculation. An optimization bi-triangle nanostructure with the bulk refractive index sensitivity of 941 nm/RIU and figure of merit of 6.8 is presented.