A type of quadrangular frustum pyramid composition nanostructure with silver in bottom layer and gold in top layer is investigated. Based on discrete dipole approximation,localized surface plasmon resonances of metal composition nanoparticles induced by optical excitation is investigated. A detail discussion is given on the extinction properties and the refractive index sensitivity of quadrangular frustum pyramid nanoparticles in different sizes,metal composition ratios and so on. The result of calculation shows that the refractive index sensitivities of quadrangular frustum pyramid composition nanoparticles with sliver layer in 50 nm thickness keep the same value as increasing the thickness of gold layer. It is also observed that the peak wavelength blue shifts as increasing the thickness of quadrangular frustum pyramid nanoparticles and red shifts as increasing the Ag concentration in the composition nanoparticles with the same shape. Especially,if the thickness of quadrangular frustum pyramid nanoparticles with structure of gold adding to silver is more than the mean free path of conduction electrons,the excitation intensity of localized surface plasmon resonances won′t change any more with increasing the thickness of added gold.