To deeply understand the formation mechanism of a critical nucleus during the nucleation process of liquid metal sodium, a system consisting of 10 000 Na atoms has been simulated by using molecular dynamics method. The evolutions of nuclei are traced directly, adopting the cluster-type index method. It is found that the energies of clusters and their geometrical constraints interplay to form the favorable microstructures during the nucleation process. The nucleus can be formed through many different pathways, and the critical size of the nucleus would be different for each pathway. It is also found that the critical nucleus is nonspherical and may include some metastable structures. Furthermore, the size of the cluster and its internal structure both play a crucial role in determining whether it is a critical nucleus, and this is in agreement with the simulations by computing the free energy of the Lennard-Jones system [D. Moroni, P. R. ten Wolde, and P. G. Bolhuis, Phys. Rev. Lett. 94, 235703 (2005)].