Two-dimensional layered silicon carbide (2d-SiC), a semiconductor with graphene-like structure, has potential applications in nonlinear optical frequency conversion. The effect of stacking and strain on the nonlinear second harmonic generation (SHG) coefficient are studied by using the first-principles calculation of the all-electron full-potential linearized augmented-plane wave combined with the sum-over-states method. The analysis of physical origin of the SHG process shows that the single-particle transition channel formed by three bands dominates the SHG process of 2d-SiC. The interband motion of electrons is significantly tuned by the intraband motion. The angle dependence of the SHG coefficient of 2d-SiC is given as a reference for future experiments. A tunable SHG enhancement could be obtained by straining 2d-SiC.