The effect of concentration on the optical nonlinearity of gold nanoparticles is investigated. Gold nanoparticles were synthesized by nanosecond-pulsed laser ablation of a high-purity gold plate in distilled water. The size of nanoparticles was measured using dynamic light scattering (DLS) method and was calculated from full width half maximum of their plasmonic absorption peak using Mie theory. Different nonlinear characteristics of gold nanoparticles are observed by considering their effects under irradiation with a second harmonic beam of a continuous-wave low power Nd-YAG laser at 532 nm. Low-power optical limiting with low limiting threshold is obtained in the sample using different apertures at different points of the laser beam path. The nonlinear optical responses are characterized by measuring the intensity dependent refractive index of medium using the z-scan technique. Results show that the linear absorption coefficient and nonlinear refractive index of samples are increased with increasing the concentration of gold nanoparticles in distilled water. Increasing the intensity of the probe beam leads to increasing the magnitude of nonlinear refractive index.