Bimetallic core-shell nanoparticles have recently emerged as a new class of functional materials because of their potential applications in catalysis, surface enhanced Raman scattering (SERS) substrate and photonics etc. Here, we have synthesized Au/Ag bimetallic core-shell nanoparticles with varying the core diameter. The red-shifting of the both plasmonic peaks of Ag and Au confirms the core-shell structure of the nanoparticles. Transmission electron microscopy (TEM) analysis, line scan EDS measurement and UV-vis study confirm the formation of core-shell nanoparticles. We have examined the catalytic activity of these core-shell nanostructures in the reaction between 4-nitrophenol (4-NP) and NaBH4 to form 4-aminophenol (4-AP) and the efficiency of the catalytic reaction is found to be increased with increasing the core size of Au/Ag core-shell nanocrystals. The catalytic efficiency varies from 41.8 to 96.5% with varying core size from 10 to 100 nm of Au/Ag core-shell nanoparticles, and the Au100/Ag bimetallic core-shell nanoparticle is found to be 12-fold more active than that of the pure Au nanoparticles with 100 nm diameter. Thus, the catalytic properties of the metal nanoparticles are significantly enhanced because of the Au/Ag core-shell structure, and the rate is dependent on the size of the core of the nanoparticles.