The phase-field model is established for precipitation transformations in multi-component alloy, which incorporates the interfacial energy and elastic energy anisotropy. The mechanism of the precipitation phase transition is revealed by means of the simulation of δ-phase precipitation process in Cu-4.0at.%Ni-2.0at.%Si alloy, and furthermore, the δ-phase precipitation kinetics is built at the temperature of 450°C. Under the influence of both interfacial energy and elastic energy anisotropy, δ-Ni2Si is presented in disc-shaped precipitates. The simulation patterns show that when one precipitate hits another precipitate with a different orientation, it stops growing, consequently forming a “T”-shape precipitate configuration. When two precipitates with the same orientations grow and hit each other, they connect or coarsen only if the spacing between the precipitates is very small. Therefore, the coarsening behavior of disc-shaped precipitate should be completely different from that of spherical precipitates.