Growth substitution of the primary Ni3Sn2 phase by peritectic Ni3Sn4 phase during solidification has been observed for the first time in directionally solidified Sn-22at.%Ni peritectic alloy. Dependence of this phase substitution phenomenon on growth distance, and thus composition of liquid phase has been confirmed, which shows significant deviations from the present understanding that the growth should be distance-independent. This substitution process is shown to arise from the continuous variation in melt concentration at the solid/liquid interface during growth of primary Ni3Sn2/peritectic Ni3Sn4 phases which are intermetallic compounds with narrow solubility ranges. An analytical model based on solute conservation during solidification has been presented to describe this phase substitution process, which gives well agreement with the experimental results. Besides, the growth distance required for phase substitution is inversely proportional to the growth velocity. It has also been demonstrated that the steady-state melt concentration could not be achieved during growth of peritectic systems containing intermetallic compounds with narrow solubility range, such as Sn-Ni peritectic alloys. This indicated that steady-state growth can not be obtained during solidification this kind of alloys.