Gold nanoparticles are considered to be better probes than the traditional polystyrene nanobeads in nanomaterials and nanobiotechnology. Meanwhile, optical tweezers are very popular tool for manipulation and force measurement in these fields. Gold nanoparticles with different size will receive radiation forces with different scale in optical tweezers. This paper theoretically studies the trapping performance of the optical tweezers for the gold nanoparticle with different size, and finally gives the relation curves between the radiation forces and the radius of the of the particle.