The lattice constants, energy band properties and formation energies of BexZn1-xO, CayZn1-yO and BexCayZn1-x-yO alloys of Be and Ca doped wurtzite ZnO alloys are calculated by the plan-wave pseudopotential method with GGA in density functional theory (DFT). The theoretical results show the lattice constants of BexZn1-xO alloy decrease with Be content increasing, which is contrary to the scenario of CayZn1-yO alloy. For the energy band properties of Be_xZn1-xO and CayZn1-yO alloys, the valence band maxima (VBM) are determined by O 2p states and the conduction band minima (CBM) is occupied by Zn 4s states, and their band gaps are broadened when Be or Ca content is increased. The lattice constant of Be0.125Ca0.125Zn0.75O alloy of Be and Ca co-doped ZnO is matched with that of ZnO and its energy bandgap is greater than that of ZnO, so Be0.125Ca0.125Zn0.75O /ZnO structure is suitable for high-quality ZnO based device. In addition, the stability of Be0.125Ca0.125Zn0.75O alloy is also analysed.