The contour intersection method is a new method used to invert the complex refractive index of small particles. Research has yet to be reported on using this method to invert the complex refractive index of nanoparticles. This paper reports the feasibility and reliability of the contour intersection method in the inversion of the complex refractive index of nanoparticles using Au-Ag alloy nanospheres. The Mie theory and the size-dependent dielectric function are used to calculate the light scattering and absorption efficiency of Au-Ag alloy nanospheres corresponding to the complex refractive index. The complex refractive index of the particles is obtained by inversion with the contour intersection method. The backscattering efficiency constraint method is used to determine the unique solution when multiple valid solutions from the contour intersection method appear. The effects of the Au component percentage, particle size, and measurement errors on the inversion results are quantitatively analyzed. Finally, the inversion accuracy is compared and analyzed with the traditional iterative method. The results show that as long as the light scattering efficiency, light absorption efficiency, and backscattering efficiency of Au nanospheres can be measured, the accurate complex refractive index can also be calculated by inversion using the contour intersection method. The accuracy of the inversion results can be ensured when the measurement error is less than 5%. The results of inversion using the contour intersection method are better than those of the iterative methods under the same conditions. This study provides a simple and reliable inversion method for measuring the complex refractive index of Au-Ag alloy nanospheres.