Using full-potential local-orbital minimum-basis method within density functional theory, we study the phase transition, electronic and magnetic properties of CsN and RbN alloys under external pressure. Concerning the phase transition, we consider three possible crystal structures, including caesium chloride (CsCl), rock salt (RS) and zinc blende (ZB) ones. Calculations of enthalpy exhibit that a pressure-induced phase transition occurs between the three structures, and the phase transitions are difficult to be distinguished under ambient condition (P = 0 GPa). As the further increase of pressure, they can be specified clearly. In addition, the electronic calculations indicate that both alloys are half-metallic ferromagnets with a total magnetic moment of 2.000 mu B, which is promising for fabricating spin injection devices. Finally, we discuss the electronic and magnetic properties of CsN and RbN under external pressure. A pressure-induced delocalized electronic states and magnetic phase transition are observed in RbN and CsN alloys.