Spectroscopic studies were carried out on monolayer, trilayer, and few layers of graphene sheets to investigate the effect of plasma parameters such as the electric current, substrate temperature, and the effect of the acetylene and hydrogen gases mixture ratios on the geometrical structure, electronic and optical properties of the synthesized films. Single-, triple- and few-layer graphene sheets were deposited on copper substrates by using self-assembled direct current plasma enhanced chemical vapor deposition (DC-PECVD) reactor. The deposited graphene samples were characterized by high resolution transmission electron microscope (HRTEM), X-ray diffraction (XRD), Raman and photoluminescence (PL) spectroscopy. The results demonstrated that the number of graphene layers as well as the defects ratio of sp2 hybridization size domain have been changed notably with changing the preparation conditions, where a single layer graphene sheet was obtained at preparation conditions of H2:C2H2 ratio of 100:4 sccm, plasma electric current of 130 mA, and substrate temperature of 750 °C. The recorded PL spectrum for the single layer graphene shows one weak and broad band at 348 nm. We have recorded an exponential relation between the blue shift of the PL peak and the changing in the size domain of the sp2 hybridization.