Based on the stability, nontoxicity, and biocompatibility of Au nanoparticles and excellent extinction properties of Ag nanoparticles, bimetallic alloy nanoparticles have potential value for applications in biosensors. In order to find alloy nanoparticles with better sensing properties, the effects of the size of Au-Ag nanoshell on Refractive Index Sensitivity, Full Width at Half Maximum, and Figure of Merit were quantitatively studied, by adopting Mie scattering theory of sphere with a concentric spherical shell and the size correction model of the dielectric function. Thus the optimal Figure of Merit and the corresponding size were obtained.Meanwhile, this article studied the effect of Au molar fraction on the optimum Figure of Merit and size was studied. The results show that when Au molar fraction x is fixed at 0.5, the Figure of Merit of Au-Ag@SiO2 nanoshell reaches its maximum value (2.09) and the corresponding core radius and shell thickness are 22.3 nm and 8.7 nm, respectively. The Figure of Merit of Au-Ag@Vacuum nanoshell reaches its maximum value (2.20) and the corresponding core radius and shell thickness are 23.6 nm and 6.9 nm, respectively. When the Au molar fraction is less than 0.25, the Figure of Merit of Au-Ag nanoshell is better than that of Au nanoshell. With the decrease of the Au molar fraction, the Figure of Merit increases to at most 2-3 times of the Au nanoshell. This study provides theoretical guidance for the effective application of Au-Ag nanoshell in the field of biosensors.