In this paper, the structural, electronic, and optical properties of the Si0.67Ge0.33 alloy have been investigated based on the density functional theory using the full-potential linearized augmented plane wave method. The structure of Si and Ge semiconductors is well known in optoelectronic applications. Recently, Si–Ge alloys have received a lot of attention. Among Si–Ge alloys, a Si0.67Ge0.33 semiconductor structure with P42/ncm space group has been studied and its structural, mechanical and thermal properties have been mainly discussed. Since the electronic and optical properties of Si–Ge alloys are very important, in addition to structural and electronic properties, some of the optical properties of Si0.67Ge0.33 alloy have been studied for the first time. Calculated lattice constants and the bulk modulus are in good agreement with reported value. Results from calculations in electronic section show that the Si0.67Ge0.33 alloy is a semiconductor with an indirect band gap of 1.4 eV. Optical properties reveal that the static dielectric function of this alloy is 11.44, and 10.59 in the x-, and z-directions, respectively. Plasmon energy of the Si0.67Ge0.33 alloy is 16.58 eV, and 16.91 eV, in the x-, and z-directions, respectively. Absorption coefficient is considerable in the visible light spectrum which is slightly greater in a x-direction than z-direction. The static refractive indexes have been obtained 3.38, and 3.31 in the x-, and z-directions, respectively.