Poly (methyl methacrylate) (PMMA) is commonly used during the transfer process of chemical vapor deposited (CVD) graphene. Since PMMA on graphene surfaces is removed by breaking polymerization backbone bonds (de-polymerization), using shorter polymer chains can be a self-solving method for PMMA residue removal. We report on graphene properties transferred with different average molecular weight poly (methyl methacrylate) (PMMA). We obtained enhanced field effect mobility and reduced hole doping without post-annealing for lower average molecular weight PMMA. Also, the graphene surfaces transferred by lower average molecular weight PMMA was free of polymer debris with clean morphology, which was confirmed by carbon 1s X-ray photoemission spectroscopy. This graphene transfer process can be used to avoid additional thermal budget which can cause degradation of device performance.