The precipitation process of Ni-Cr-Al alloy with low Al content was studied at atomic scale based on the microscopic phase-field kinetic model coupled with elastic strain energy. The aim is to investigate the effect of elastic strain energy on precipitation mechanism and morphological evolution of the alloy. The simulation results show that in the early stage of precipitation, D022 phase and L12 phase present irregular shape, and they randomly distribute in the matrix. With the progress of aging, L12 phase and D022 phase change into the quadrate shape and their orientations become more obvious. In the later stage, L12 phase and D022 phase present quadrate shape with round corner and align along the [100] and [010] directions, and highly preferential selected microstructure is formed. The mechanism of early precipitation of L12 phase in Ni-17%Cr-7.5%Al (mole fraction) alloy is the mixed style of non-classical nucleation growth and spinodal decomposition and the D022 phase is the spinodal decomposition. The mechanisms of early precipitation of L12 phase and D022 phase in Ni-12.5%Cr-7.5% Al alloy are both the non-classical nucleation and growth. The coarsening process follows the rule of preferential selected coarsening.