We report the giant enhanced optical harmonic generation in all-dielectric silicon nitride (SiN) based resonant waveguide gratings (RWGs) of quasi-bound states in the continuum (BICs) of ultra-high Q factor and localized field. The BICs are realized by tuning the excitation of the guided modes modulated by geometry parameters of four-part grating layer. At a feasible structure of quasi-BIC for nanofabrication, the SHG and THG are enhanced by 103 and 106, compared with those from the RWGs of traditional two-part grating layer, respectively, and even up to 108 and 1010 compared with those from the planar SiN film, respectively. The resonance wavelength of quasi-BICs can be effectively tuned by the angle of incidence, while almost not affect the enhancement of SHG and THG response. Our results show that the efficiency harmonic generation from all-nonlinear-dielectric RWGs of quasi-BICs has potential applications for the integrated nonlinear photonic devices.