The mechanism of low-temperature deformation in a fracture process of L12 Ni3Al is studied by molecular dynamic simulations. Owing to the unstable stacking energy, the [01̄1] superdislocation is dissociated into partial dislocations separated by a stacking fault. The simulation results show that when the crack speed is larger than a critical speed, the Shockley partial dislocations will break forth from both the crack tip and the vicinity of the crack tip; subsequently the super intrinsic stacking faults are formed in adjacent {111} planes, meanwhile the super extrinsic stacking faults and twinning also occur. Our simulation results suggest that at low temperatures the ductile fracture in L12 Ni3Al is accompanied by twinning, which is produced by super-intrinsic stacking faults formed in adjacent {111} planes.