We report the diffraction behavior of harmonic generation in metasurfaces of quasi-bound states in the continuum (BICs) induced by geometrical perturbations. Conventionally, the geometrical perturbation can transform the symmetry-protected BICs into quasi-BICs in metasurfaces for many important applications. Such geometrical perturbations sometimes lead to the doubled period of metasurfaces, and then dramatically affect the diffraction of light, especially the harmonic generation light of shorter wavelengths. Here, we investigate the efficiency and diffraction angles of different orders of second and third harmonic generation in two typical metasurfaces of quasi-BICs induced by geometrical perturbation, i.e., compound grating waveguide nanostructures and zig-zag nanodisk arrays. The results are important to understand the diffraction behavior of harmonic generation in the period doubled or tripled nanostructures due to geometry perturbations, and to realize the efficient multi-channel nonlinear sources.