Transfer method of chemically vapor deposition graphene is an appealing issue to realize its application as flexible and transparent electrodes. A universal stamping method to transfer as grown graphene from copper onto different flexible and transparent polymers (FTPs) reported here ensures simple, robust, rapid, clean and low-cost. This method relies on coating ethylene vinyl acetate (EVA) onto the as grown graphene, binding EVA coated graphene/Cu with FTPs and delamination by hydrogen bubbling process, which is analogous to the method used by stamping process where ink carries the imprint of the object onto any materials. The fate of the stamping method depends on how strongly the adhesion of EVA coated graphene/Cu with target FTPs. Interestingly, we have found that the thin film of EVA/graphene/Cu can only bind strongly with the FTPs of less than 25 µm in thickness and lower glass transition temperature value to the EVA while wide range of other FTPs are considered upon surface engineering to enhance the binding strength between FTPs and EVA. What's more, the electrical performance was investigated with a demonstration of triboelectric nanogenerators which confirmed the reliability of graphene transfer onto the FTPs and prospect for the development of flexible and transparent electronics.