The fundamental issues related to the formation of mechanical cracks and the chemical residue during the transfer process of large-area CVD graphene by polymeric carrier-films are addressed in this work. This paper presents a method to design a new polymer carrier-film (using polystyrene (PS) and 4,4'-diisopropylbiphenyl (DIPB)) that is free from mechanical cracks and polymer residue during the transfer of large-area graphene from a metal catalyst. This new polymer carrier film shows excellent mechanical flexibility and good solubility in tetrahydrofuran solvent without any residue and it is confirmed that the graphene transfer process is excellent without mechanical destruction even over a large area. Our result gave a technical milestone for the real industrial application of graphene in many application areas (not only graphene but also several two-dimensional materials such as boron nitride, transition metal di-chalcogenide, and black phosphorus).