Graphene is epitaxially grown on vicinal SiC(0001) surfaces via high temperature annealing in vacuum. To obtain higher quality graphene films and to investigate growth mechanisms it is beneficial to use well-defined SiC surface structures, which can be achieved by high temperature hydrogen etching before graphitization. The SiC surfaces with the periodic nanofacet structure resulted from the etching are thermally decomposed and graphitized to form epitaxial graphene layers. Temperature and time dependences of graphene growth are mainly investigated by means of low energy electron microscopy (LEEM). The graphene growth is accomplished by the layer-by-layer mode with strong anisotropy in the direction parallel to the steps and is limited by Si desorption from the surface/interface, where the 0th layer (buffer layer) is nucleated.