The thermal decomposition of SiC surface provides, perhaps, the most promising method for the epitaxial growth of graphene on a material useful in the electronics platform. Currently, efforts are focused on a reliable method for the growth of large-area, low-strain epitaxial graphene that is still lacking. We report here a novel method for the fast, single-step epitaxial growth of large-area homogeneous graphene film on the surface of SiC(0001) using an infrared CO2 laser (10.6 {mu}m) as the heating source. Apart from enabling extreme heating and cooling rates, which can control the stacking order of epitaxial graphene, this method is cost-effective in that it does not necessitate SiC pre-treatment and/or high vacuum, it operates at low temperature and proceeds in the second time scale, thus providing a green solution to EG fabrication and a means to engineering graphene patterns on SiC by focused laser beams. Uniform, low-strain graphene film is demonstrated by scanning electron microscopy and x-ray photoelectron, secondary ion mass, and Raman spectroscopies. Scalability to industrial level of the method described here appears to be realistic, in view of the high rate of CO2-laser induced graphene growth and the lack of strict sample-environment conditions.