The transfer of CVD-grown graphene sheets onto arbitrary substrates is important for the development of practical applications. Unfortunately, designing a low cost and highly efficient graphene transfer technique to achieve defect-free graphene sheets with low contact resistance onto various substrates still remains a challenge. In this paper, a CVD grown monolayer graphene sheet was directly transferred on SiO2/Si substrate. We found that a combination of floating copper with graphene films on ammonium persulfate solution with an original method of supercritical CO2 fluid can effectively produce clean and dry samples without damaging the crystalline quality of graphene. This method does not require any polymeric material to be desposited on the graphene films at any stage. Samples are analyzed by optical microscopy, Raman spectroscopy, scanning electron microscopy and atomic force microscopy. This method is very promising for cleaning graphene samples for electronic device fabrication.