The electronic and optical properties of graphene monoxide, a new type of semiconductor materials, are first theoretically studied based on density functional theory. Electronic calculations show that the band gap is 0.952 eV which indicate that graphene monoxide is a direct band gap semiconductor. The density of states of graphene monoxide and the partial density of states for C and O are given to understand the electronic structure. In addition, we calculate the optical properties of graphene monoxide including the complex dielectric function, absorption coefficient, the complex refractive index, loss-function, reflectivity and conductivity. These results provide a physical basis for the potential applications in optoelectronic devices.