Abstract: With first-principles density functional theory（DFT） based on plane-wave pseudopotential method, we have calculated and analyzed the electronic structure and optical properties of wurtzite AlN and sphalerite AlN. In computational detail, generalized gradient approximation（GGA） works with Norm-conserving pseudopotential and local-density approximation（LDA） works with Ultrasoft pseudopotential, respectively. The lattice constant, band gap width, reflectance, refractive index and absorption coefficient of the two structures AlN obtained by the two methods are analyzed and compared. The comparison results show that LDA’s band gap error of two methods is smaller and more consistent with the experimental values, and the calculated optical properties of wurtzite AlN show that GGA is closer to the experimental value, for the optical properties of sphalerite AlN, LDA is closer to the experimental value.