Gold clusters with the sizes close to the Fermi wavelength of electron shows interesting quantum size effects. Linear and nonlinear optical properties show dramatic trends when the sizes of clusters are in the range of quantum confinement. We have investigated the size dependence of the non-linear optical property of two-photon absorption (TPA) cross-sections of the gold clusters. Absolute TPA cross-sections are measured by a combination of one and two-photon excited fluorescence upconversion measurements. Large cross-sections and abrupt changes in the trend of cross-sections are observed in the size-dependence when size is reduced from nanoparticles to cluster. The results can be attributed to the appearance of quantum confinement in these monolayer protected gold clusters.