As a nanoscale coherent light source, semiconductor nanolaser is a key device for future optoelectronic integrated chips. The obstacle of further miniaturization of the nanolaser is that the loss increases rapidly with the decrease of cavity volume. The bound states in the continuum (BICs) can overcome the high radiative loss. Here, we propose a nanolaser based on quasi-BIC mode supported by all-dielectric resonant waveguide grating (RWG), which can effectively reduce the threshold of nanolaser. The quasi-BIC mode of the waveguide can be excited when the traditional two-part grating becomes a four-part grating. The laser behavior of the quasi-BIC is studied by finite difference-time-domain (FDTD) numerical simulation. The results show that the threshold of the naolaser based on four part-grating RWG is 20.86% lower than that of nanolaser based on two part-grating RWG when subjected to TE-polarized light irradiation. For the TM-polarized light irradiation, the threshold is 3.3 times lower than the threshold for the nanolaser based on four part-grating RWG. We also find that the threshold of the nanolaser under TE-polarized light irradiation is about one order of magnitude lower than that under TM-polarized light irradiation. Because the electric field of the structure is well confined inside the waveguide layer under TE-polarized light, which can enhance the interaction between light and gain materials and reduce the threshold of nanolasers.