In this paper, the electronic structures and optical properties of two-dimensional carbonaceous graphene, graphdiyne are studied based on density functional theory (DFT). The results reveal that the graphene is more stable than the graphdiyne. In the vicinity of Fermi level, the electronic states of grapheme and graphdiyne are mainly contributed by the C-2p state. The graphene exhibited better non-linear optical absorption properties and electrical conductivity under the visible light conditions. However, graphdiyne has excellent optical absorption and electrical conductivity in the range of partial infrared light. In addition to the transition from valence-band to conduction-band, there is also the inner-band transition near the Fermi level. The conclusion can provide theoretical basis for the application of two-dimensional carbon material grapheme and graphdiyne in optoelectronic devices and photocatalysi.