Crystallization of amorphous Na is simulated by using the molecular dynamics method, and the evolutions of atomic clusters are traced by the cluster-type index method (CTIM) we proposed previously. It is demonstrated that the crystallization process exhibits three distinct stages of nucleation, subsequent growth of nuclei and coarsening of crystal grains. Both the size and the inteal structure of a cluster play crucial roles in determining whether it is a nucleus. The cluster tracing analysis can identify different crystallization stages more clearly and accurately than other methods. Meanwhile, the simulation results can provide a reasonable explanation at an atomic level for the experimental phenomenon obtained previously.