The properties of graphene vary with the number of layers, thus determining its usefulness in different applications. Consequently, it is important to develop a method for precisely controlling the number of layers for various application demands. In this study, high quality monolayer graphene was successfully prepared using pulsed laser deposition. Meanwhile, the growth of monolayer and bilayer graphene can be controlled by adjusting the laser energy density. Raman spectra show that high quality monolayer films grew at a laser energy density of 5.66 J/cm(2) and bilayer graphene films grew at a laser energy density of 8.49 J/cm(2). X-ray photoelectron spectroscopy indicate that the main chemical state of carbon is the sp(2) hybrid state, and the maximum atomic ratio of sp(2) and sp(3) results from the sample with laser energy density of 5.66 J/cm(2). Scanning electron microscope images show that monolayer graphene is connected by small sheets with different sizes, and the largest graphene sheet reaches 20 mu m. High resolution transmission electron microscope images and selected area electron diffraction patterns show that graphene samples are highly crystalline and yield significant layer information. UV-Vis spectra indicate that the transmittance through monolayer and bilayer graphene at 550 nm are 96.93% and 95.05%, respectively. Ultraviolet photoelectron spectroscopic measurements show that the work function of graphene ranges from 3.72 eV to 4.76 eV; the variation in the work function is related to growth defects. Finally, the relationship between the structure of the graphene films and laser energy density are investigated in detail, and these results indicate that the controllable growth of graphene can be achieved by adjusting the laser energy density. This means that a suitable laser energy density is conducive to defining an equilibrium between diffusion and condensation of carbon atoms, which is crucial to the growth of high-quality monolayer and bilayer graphene. It is expected that this study might be facilitate the preparation of graphene-based composite films and devices.