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 Au-Cu-Al ternary system is a well-known HumeRothery electron compound, which may present a shape memory effect [1] . This alloy also displays attractive glittery surface patterns after martensitic transformation, so, the alloy is named "spangold" [2] . During the cooling, the alloy undergoes A2→B2→L2 1 ordering transitions and subsequent martensitic transformation. Extensive experiments show that the martensitic transformation cannot occur unless the parent phase is in the L2 1 structure and the ordering degree makes a significant effect on the martensitic transformation [3] . The nature of the ordering transition process and the critical transition temperature of B2→L2 1 , however, are still unclear, for the A2→B2 and B2→L2 1 ordering transitions are coupled and cannot be separated from each other easily.Recently, multiple techniques and measurements, e.g. thermal analysis, electrical resistivity and internal friction, are employed to characterize the B2→L2 1 transition [3] . Besides, the experimental results for AuCu-Al systems also have motivated several recent studies employing Bragg-Williams-Gorski (BWG) model to analyze the ordering transition [4] . Whereas the experimental and theoretical studies confirmed the existence of B2→L2 1 ordering transition, the microcosmic mechanisms of the phenomenon is ambiguous. And the static BWG model cannot illustrate the transition processes on cooling treatment. Therefore, in present paper, we apply a generalized lattice model and Monte Carlo simulations in the study of B2→L2 1 ordering transition. The mixing potentials based on Connolly-Williams methods are constucted from the total energies of a series of Au 2 Cu 1−x Al 1+x (−0.15 x 0.15) ordered structures. Subjecting the mixing potentials to Monte Carlo simulations, the order-disorder transition temperature of the Au 2 Cu 1−x Al 1+x is also obtained and compared with experiments.