Boiling heat transfer (BHT) is a particularly efficient heat transport method because of the latent heat associated with the process. However, the efficiency of BHT decreases significantly with increasing wall temperature when the critical heat flux (CHF) is reached. Graphene has received much recent research attention for applications in thermal engineering due to its large thermal conductivity. In this study, graphene films of various thicknesses were deposited on a heated surface, and enhancements of BHT and CHF were investigated via pool-boiling experiments. In contrast to the well-known surface effects, including improved wettability and liquid spreading due to micron- and nanometer-scale structures, nanometer-scale folded edges of graphene films provided a clue of BHT improvement and only the thermal conductivity of the graphene layer could explain the dependence of the CHF on the thickness. The large thermal conductivity of the graphene films inhibited the formation of hot spots, thereby increasing the CHF. Finally, the provided empirical model could be suitable for prediction of CHF.