By using the discrete-dipole approximation, we computed the extinction spectrum of a gold-silver alloy nanoparticle. We have examined how the surface plasmon resonance changes with respect to the variation in the composition of the alloy particle. As the fraction of silver increases for a 10nm particle, the peak position of the extinction spectrum blue-shifts linearly. The intensity of the peak however increases exponentially with increasing the silver fraction. These results are in accord with the previous experimental results.