It is difficult to obtain bulk amorphous alloys experimentally due to the limitation of cooling technology and the ability to form amorphous alloy. However, the rapid cooling of nano-droplets is relatively easy, so the simulation research of nano-droplets is easier to verify experimentally. In this work, the molecular dynamics simulation for the rapid cooling of Cu₆₄Zr₃₆ nano-droplets of different sizes is conducted at a cooling rate of 1.0 × 10¹² K/s, and the evolution of microstructure is analyzed in terms of the average potential energy, the pair distribution function, the three-dimensional visualization, and the largest standard cluster analysis. The analysis of the energy curves and the characteristic length for short-range-ordered microstructure show that the solidification process for all nano-droplets undergoes liquid-liquid transition and liquid-solid transition, and finally forms amorphous nanoparticles. Comparing with the icosahedron, the evolution of the topologically close-packed (TCP) structures can reflect the basic characteristics of phase transitions effectively. Based on the evolution of TCP clusters, the entire solidification process of nano-droplets can be divided into four stages: embryo, aggregation, growth and coarsening. The TCP structure embodies the basic structural characteristics of amorphous nano-droplets and particles, which is of great significance in perfecting the solidification theory.