The effects of stacking periodicity on the electronic and optical properties of GaAs/AlAs superlattice have been explored by density functional theory calculations. Among the (GaAs)m/(AlAs)m, (GaAs)1/(AlAs)m and (GaAs)m/(AlAs)1 (m = 1 to 5) superlattices, the band gaps of (GaAs)m/(AlAs)1 superlattices decrease significantly as the layer of GaAs increases, and the cut-off wavelengths are found to locate in the near infrared region. For (GaAs)m/(AlAs)1 SLs, the conduction bands shift toward Fermi level, resulting in the smaller band gap, while conduction bands of (GaAs)1/(AlAs)n SLs slightly shift to higher energy, which lead to comparable band gaps. The layer number of GaAs shows negligible effects on the reflectivity spectra of superlattice structures, while the absorption coefficient shows a red-shift with the increasing layer of GaAs, which is beneficial for the application of GaAs/AlAs superlattice in the field of near infrared detector. These results demonstrate that controlling the number of GaAs layers is a good method to engineer the optoelectronic properties of GaAs/AlAs superlattice.