The B2-L21 ordering transitions in Au-Cu-Al shape-memory alloys are studied by the Monte Carlo exchange simulations,where a set of the first,the second and the third nearest-neighbor mixing potentials for CuAl in the Au-Cu-Al alloys are calculated from first principals using the Connolly-Williams methods.To ensure the phase stability of the β-Au-Cu-Al,the investigation includes the range of compositions Au2Cu1-xAl1+x (0.15≤x≤0.15).The B2-L21 transition temperatures are predicted,and are in agreement with the experimental results.The atomic ordering around vacancy of the L21 structure is further discussed. The B2-L21 ordering transitions in Au-Cu-Al shape-memory alloys were studied by the Monte Carlo exchange simulations, where a set of the first, the second and the third nearest-neighbor mixing potentials for CuAl in the Au-Cu- Al alloys are calculated from first principals using the Connolly-Williams methods. To ensure the phase stability of the β-Au-Cu-Al, the investigation includes the range of compositions Au2Cu1-xAl1 + x (0.15 ≦ x ≦ 0.15). B2-L21 transition temperatures are predicted, and are in agreement with the experimental results. Atomic ordering around vacancy of the L21 structure is further discussed.