First-principles calculation is a quite powerful tool for explaining experimental phenomena and predicting the properties of new materials. Based on the first-principles calculation within the density functional theory, the energetic stabilities and electronic properties of Mg and Si doped GaN/AlN superlattices with wurtzite and zinc-blende structures are investigated. The results show that there is no variation in formation energy if the doping position is changed when the impurities are doped in the well (GaN) region, and the same situation also happens in the barriers (AlN) region. Thus it is equivalent for dopants to replace Ga atoms in the cation site of wells or Al atoms in the cation site of barrers. However, the formation energies of these dopants in the well region and the barrier region are different. Compared with the formation energy in the barrier region, it is much lower in the well region. That is to say, the impurities in the cation site (MgGa, MgAl, SiGa and SiAl) present lower formation energies in the wells of GaN/AlN SLs with wurtzite and zinc-blende structures. In addition, the impurities in zinc-blende GaN/AlN superlattices present lower formation energy than in the wurtzite structure. The negative formation energy illustrates that the defects are spontaneously formed if Mg-atom is mixed into the wells of the zinc-blende structure. Therefore, in experiment, for the zinc-blende superlattice structure, preparing p-type semiconductor needs less energy than preparing n-type semiconductor. And for the wurtzite superlattice structure, preparing p-type semiconductor needs the same energy as preparing n-type semiconductor. Furthermore, the relationships between the distribution of the electronic states and their structures are analyzed. It is found that the different kinds of dopants lead to different band bendings, owing to the modified polarization fields. The spatial distributions of electrons and holes, plotted by the partial charge densities, reveal that electrons and holes experience redistributions by Si or Mg dopants in different phases. The band gap of doped GaN/AlN superlattice decreases and the projected density of states also accounts for the change of defect formation energy. The calculated results provide a new reference for the fabrication of modulation-doping GaN/AlN SL under desired control, which could be considered to control phase.