Cubic silicon carbide has enough potential for high power and high frequency devices with low loss. In order to achieve such devices, thick, smooth surface, low-doped and high crystal quality epitaxial layers are needed. In order to obtain such layers, homoepitaxial growth was carried out by sublimation epitaxy on cubic silicon carbide substrates. The surface of cubic silicon carbide layers grown at the growth rate of 42 mum/h was very smooth and comparable to that of alpha-silicon carbide. The crystal quality of epitaxial layers was better than that of substrates. However, much impurity such as aluminum and nitrogen was observed by the photoluminescence.