We investigate second harmonic generation (SHG) in all-dielectric resonance nanostructures of high-Q factors assisted by quasi-bound states in the continuum (quasi-BICs). The typical resonators, e.g., guided-mode resonance gratings and asymmetric metasurfaces, fabricated by AlGaAs were numerically studied with the consideration of nonlinear refraction of AlGaAs. The resonance peak and line-shape of linear transmission and SHG spectra in the resonators can be dramatically changed under intense pump intensities. The SHG conversion efficiency in the nanostructures working at quasi-BICs is much lower than the traditionally expected values without considering the nonlinear refraction of dielectrics. The ultimate SHG conversion efficiency is finally obtained. The investigation has the significance for the design and understanding of efficient nonlinear metasurfaces of high-Q factors.