The rapid solidification process of liquid Cu64Zr36 alloy is simulated using a molecular dynamics method. The evolution in micro-structures are analyzed by means of pair distribution functions (PDF), Honeycutt-Andersen (H-A) bond-type index method and cluster-type index method (CTIM). It is found that both of liquid and rapidly solidified solid mostly consist of (12 0 12 0) icosahedra and their distorted (12 8/1551 2/1541 2/1431) configurations at a cooling rate of 50 K/ns, most of which are Cu-centered Cu8Zr5 clusters, followed by Cu7Zr6 and then Cu9Zr4 clusters. Size distribution of icosahedral medium-range order (IMRO) clusters linked by intercross-sharing (IS) atoms in the liquid and the glassy solid presents the magic number sequences of 13, 19, 25,···and 13, 19, 23, 25, 29, 37···, respectively. The track of atoms reveals no icosahedral clusters in rapidly solidified solid that can be detected in the liquid alloy. Onset temperature of configuration heredity emerges in the supercooled liquid region of Tm–Tg. A direct and perfect heredity of icosahedra is found to be dominant and a distinct ascent in heredity fraction takes place at Tg. Compared with (12 8/1551 2/1541 2/1431) distorted icosahedra, (12 0 12 0) standard icosahedra are of high structural stability and configurational genetic ability below Tg, whereas only a few can keep their chemical composition unchanged. By partial heredity, even some IMRO clusters in super-cooled liquid can be transmitted to glassy alloy.