Low-cost large-diameter cubic silicon carbide (3C-SiC) film grown on silicon (Si) has been demonstrated to have a wide range of applications in photonics, electronics, photoelectrochemistry and micro-electro-mechanical system technologies. In this paper, the epitaxial growth of SiC on Si by low-pressure chemical vapour deposition is investigated. Two modes were employed to supply the precursors: the alternating supply and the simultaneous supply. Compared with SiC films grown at the same temperature by simultaneous supply epitaxy method, the SiC grown by alternating supply epitaxy (ASE) method has better crystallinity, smoother surface, and better thickness uniformity as confirmed by X-ray diffraction and atomic force microscopy characterisation. We propose the growth mechanism for ASE growth of 3C-SiC and validate it in detail experimentally. It is found that, Si deposition on SiC follows either Stranski–Krastanov mode or island growth mode, while SiC formation proceeds in two possible reaction paths: redistributing of the formed Si islands or smoothing of the formed SiC islands by decomposition migration process. Both reaction paths are driven by minimizing the surface free energy and reducing dangling bonds density. In summary, the key features of ASE are: (1) Si has a longer diffusion length and thus higher probability to adhere to a crystallographically favourable position; (2) undesirable gas phase reactions can be avoided. The obtained results indicate that ASE is a unique and economically viable method to prepare uniform 3C-SiC on multiple large-diameter Si wafers.