The beta-Si3N4 crystals are widely used in industrial and electronics areas. Therefore, beta-Si3N4 has drawn the attention of researchers for many years. In this study, effects of icosagen group impurity atoms in the IIIA group on the electronic properties of the beta-Si3N4 crystal were analyzed by using the density functional theory. As a result of these analyses, it was determined that the electronic properties of the crystal change significantly. Basic electronic characteristics for pure beta-Si3N4 crystal and icosagen group impurity beta-Si3N4 crystals, such as band structures, densities of states, binding energies, and formation energies were investigated. We identified that the band gap of the beta-Si3N4 crystal was affected significantly by the impurity, and this change was varying linearly in line with the formation energy for the impurity cases. As a result of calculations, the Al-impurity was found to be the lowest-energy impurity state.