Graphene films grown on metal substrates by chemical vapor deposition (CVD) method have to be safely transferred onto desired substrates for further applications. Recently, a roll-to-roll (R2R) method has been developed for large-area transfer, which is particularly efficient for flexible target substrates. However, in the case of rigid substrates such as glass or wafers, the roll-based method is found to induce considerable mechanical damages on graphene films during the transfer process, resulting in the degradation of electrical property. Here we introduce an improved dry transfer technique based on a hot-pressing method that can minimize damage on graphene by neutralizing mechanical stress. Thus, we enhanced the transfer efficiency of the large-area graphene films on a substrate with arbitrary thickness and rigidity, evidenced by scanning electron microscope (SEM) and atomic force microscope (AFM) images, Raman spectra, and various electrical characterizations. We also performed a theoretical multiscale simulation from continuum to atomic level to compare the mechanical stresses caused by the R2R and the hot-pressing methods, which also supports our conclusion. Consequently, we believe that the proposed hot-pressing method will be immediately useful for display and solar cell applications that currently require rigid and large substrates.