In this paper, the effects of doping elements（Re and Ru）content on the stability and occupancy orientation of a Ni-Al binary model nickel-based single-crystal superalloy are studied by using first-principles calculations. The results show that the total energy of the system decreases gradually with the increase of the content of Re and Ru elements, which suggests that the stability of the system is improved. The system using Ru to replace Ni has the lowest stability, while the stability of system is the best by using Re to replace Al. Therefore, Re and Ru are more inclined to replace Al, which is consistent with the previous experimental results. Meanwhile, compared to other contents of Re and Ru, when Re and Ru with the content of about 1.4% are used to replace Al, the substitution formation energy is the lowest. Furthermore, two different stacking fault modes are obtained by deleting a layer of atoms in the Ni-Al binary model. Research on these two stacking fault modes indicates that replacing Al with Re and Ru can improve the stability of the systems, and systems containing Re are more stable, which have lower substitution formation energy compared to replacing Al with Ru. However, for different stacking fault modes, when replacing Al with Re and Ru, the content of Re and Ru is different for the best of a stable system and the lowest of substitution formation energy and stacking fault energy. Replacing Al with Re results in a better stability in stacking fault systems, but the content of Re in the most stable system depends on the selected stacking fault mode.