The precipitation process of Ni₇₅Al₁₅Ti₁₀ alloy was simulated by microscopic phase-field kinetics model. The microscopic morphology evolution is firstly studied, which indicates that the precipitation process has been divided into two stages: the first is the transformation from L1₀ phase to L1₂ phase, the second is the formation of stoichiometric L1₂ phase. The effect of single aging temperature on the microstructure and atomic occupation probability and atomic diffusion are subsequently investigated. The result shows that the shape of γ′ precipitates is transformed from irregular shape to regular cuboid and the degree of orientation growth enhances with the increasing of aging temperature. But the higher aging temperature, the lower occupation probability and lower order degree. Meanwhile, the path of diffusion of Al is from the interface to the internal of γ" phase, and the diffusion of Ti atom is the opposite. Furthermore, we further study the dual aging with the purpose of improving occupation probability of γ′ precipitates and discuss its influence on the γ′ phase. Dual aging can not only obtain stable γ" phase with regular shape, but also can increase the occupation probability of Al and Ti and inhibit the formation of anti-site defects. Our results provide useful information in preparing Ni-Al-Ti alloy with excellent mechanical properties to some extent.