We demonstrate a polymer-free method that can routinely transfer relatively large-area graphene to any substrate with advanced electrical properties and superior atomic and chemical structures as compared to the graphene sheets transferred with conventional polymer-assisted methods. The graphene films that are transferred with polymer-free method show high electrical conductance and excellent optical transmittance. Raman spectroscopy and X-ray/ultraviolet photoelectron spectroscopy also confirm the presence of high quality graphene sheets with little contamination after transfer. Atom-resolved images can be obtained using scanning tunneling microscope on as-transferred graphene sheets without additional cleaning process. The mobility of the polymer-free graphene monolayer is as high as 63,000 cm(2) V(-1) s(-1), which is 50% higher than the similar sample transferred with the conventional method. More importantly, this method allows us to place graphene directly on top of devices made of soft materials, such as organic and polymeric thin films, which widens the applications of graphene in soft electronics.