We investigate systematically the competition between the second harmonic generation (SHG) and two-photon-induced luminescence (TPL) that are simultaneously present in Au nanoparticles excited by using a femtosecond (fs) laser. For a large-sized (length ~ 800 nm, diameter ~ 200 nm) Au nanorod, the SHG appears to be much stronger than the TPL. However, the situation is completely reversed when the Au nanorod is fragmented into many Au nanoparticles by the fs laser. In sharp contrast, only the TPL is observed in small-sized (length ~ 40 nm, diameter ~ 10 nm) Au nanorods. When a number of the small-sized Au nanorods are optically trapped and fused into a large-sized Au cluster by focused fs laser light, the strong TPL is reduced while the weak SHG increases significantly. In both cases, the morphology change is characterized by scanning electron microscope. In addition, the modification of the scattering and absorption cross sections due to the morphology change is calculated by using the discrete dipole approximation method. It is revealed that SHG is dominant in the case when the scattering is much larger than the absorption. When the absorption becomes comparable to or larger than the scattering, the TPL increases dramatically and will eventually become dominant. Since the relative strengths of scattering and absorption depend strongly on the size of the Au nanoparticles, the competition between SHG and TPL is found to be size dependent.