Based on the microscopic phase-field kinetic model, the growth of the ordered phase and the growth direction change of the structure during the early precipitation for Ni-Al-V alloys with different components when aging were investigated. The results show that during the early precipitation the competitive growth between ordered phases may greatly influence the shape and growth direction of alloys. Under the condition of certain temperature and elastic stress, when the Al content is lower, DO22 ordered phases precipitate first, which are numerous and small, the rafting of the ordered phase is not obvious and there is not remarkable rafting for the whole alloys. When the Al content a little higher, L12 phases precipitate first, DO22 phases become less and bigger, and the structure preferentially grows along [100]. When the Al content is much higher, L12 phases precipitate first, and the DO22 phase becomes less and bigger continuously, while the structure exhibits a strong rafting trend along [100]. Aged at a lower temperature, L12 ordered phase precipitates ahead and the rafting trend is weaker