The nucleation mechanism of Ti₃Al alloy is simulated by the molecular dynamics method in this work. The atomic clusters on different spatial scales are identified in the solidification process by the cluster-type index method (CTIM), and the formation process and the growth process of critical nucleus are studied in depth. It is found that the solidification system contains ten thousands of different types of atomic cluster structures, but only 22 types play a key role in the nucleation process. In the nucleation and growth process of nuclei, the ICO-like cluster, the BCC-like cluster, and the defective FCC cluster and the defective HCP cluster respectively reach their saturation points at the characteristic temperature T₁ (1110 K), T₂ (1085 K) and T₃ (1010 K). And the competition processes of these clusters are revealed according to the changes of their number and spatial distribution with temperature. By tracing the nucleation and growth process of the grain with parallel twin, it is found that the critical crystal nucleus is composed of single-phase FCC structures, and the preferent nucleation of metastable bcc structure is not observed. The twinned structure is formed by the layer-by-layer growth along the close-packed plane. It is also found that the CTIM is more accurate than other methods in revealing the microstructural characteristics during the solidification.