The bound state in the continuum (BIC) found in artificial microstructures such as photonic crystals is located above the light cone but not couples with the background leakage modes, and therefore it has an infinite Qfactor, making lasers working at BICs or quasi-BICs have the advantage of low threshold. And low-contrast grating is often used in the mode modulation and out coupling of low-cost lasers. For the simplified three-layer slab structure of the lasers, it is proposed to induce a quasi-BIC with the Qfactor of 9.2×10⁵ by etching the low-contrast grating (LCG) in the top cladding layer. Besides, it is found the thickness of active layer is more sensitive to quasi-BIC lasers than the depth of etched LCG, and the Qfactor can be maximized periodically up to 9.66×10⁶ with the increase of the thickness of bottom cladding layer. The results are instructive to the design of grating-based low threshold electrically injected surface-emitting lasers.