The crystallization processes of liquid Cu on single crystal Ta and amorphous Ta under different undercoolings were investigated with molecular dynamics simulation. As the undercooling is not greater than 350 K, only heteronucleation process occurred in both cases. However, at a larger undercooling (400 K), the nucleation transformed from a heteronucleation mode to a mix-mode of heteronucleation and homonucleation in both cases. Interestingly, we found that the heteronucleation of Cu embryos, in the amorphous-Ta/liquid-Cu samples, was always triggered by the recrystallization of amorphous Ta; it means that crystal Ta possesses a higher nucleation potency than amorphous Ta. Further analysis indicated that the higher nucleation potency of single crystal Ta originates from its ability to induce liquid Cu atoms ordering. Liquid Cu took a longer time, on average, to nucleate on amorphous Ta than on crystal Ta at different temperatures. In addition, microstructure analysis indicated that the crystallized region contained both stacking faults and twin crystals.