The solidification properties of liquid Na during the crystallization process have been investigated at the microscopic level by using the molecular dynamics method. According to the evolutions of thermodynamic, structural and dynamic properties for liquid Na, its crystallization process below melting temperature Tm can be divided into three transition stages. The cluster tracing analyses based on the cluster-type index method show that both the cluster size and its internal structure determine whether it is a critical nucleus. The critical nucleus contains a metastable phase and possesses a non-spherical shape. The crystallization kinetic properties obtained from the atomic level by means of the cluster tracing analyses are in agreement with the basic solidification theory.