Graphene directly grown on an 4H-SiC (0 0 0 1) substrate by chemical vapor deposition was studied: it was shown that Si evaporation process is not completely halted during graphene growth when TG 1400 degrees C, the SiC substrate decomposes at the position of graphene coverage. AFM and Raman spectrum results reveal that carbon concentration significantly influences graphene growth rate and morphology/structure. It is found that the quality of graphene film depends on the growth temperature and the flow of carbon source. We develop a new gradient growth method to produce a feasible graphene material for electronic devices. Graphene grown by this method has a flat-morphology structure, low wrinkle density, high crystal quality, good uniformity, and outstanding electrical transport properties. Nitrogen doping has an n-type doping effect on graphene carrier concentration. The main component of nitrogen-bond type is the graphitic configuration. The graphene material with nitrogen doping reaches a record mobility of 9010 cm(2)/V.s by room temperature Hall effect measurement, indicating graphene grown by gradient method with suitable nitrogen doping could yield a high quality film comparable to that by traditional method.