A three-dimensional kinetic Monte Carlo (KMC) model has been developed to study the step instability caused by nucleation during the step-flow growth of 3C-SiC. In the model, a lattice mesh was established to fix the position of atoms and bond partners based on the crystal lattice of 3C-SiC. The events considered in the model were adsorption and diffusion of adatoms on the terraces, attachment, detachment and interlayer transport of adatoms at the step edges, and nucleation of adatoms. Then the effects of nucleation on the instability of step meandering and the coalescence of both islands and steps were simulated by the model. The results showed that the instability of step meandering caused by nucleation was affected by the growth temperature. And the effects of nucleation on the instability was also analyzed. Moreover, the surface roughness as a function of time for different temperatures was discussed. Finally, a phase diagram was presented to predict in which conditions the effects of nucleation on step meandering become significant and the three different regimes, the step-flow (SF), 2D nucleation (2DN), and 3D layer by layer (3DLBL) were determined.