Structural and bonding transformation of the Al0.67CrCoFeNi high-entropy alloys (HEA) during quenching is investigated by molecular dynamics simulations. At a high cooling rate, some short-ranged ordered clusters, such as FCC, HCP and BCC crystalline clusters are already present in the almost amorphous HEAs. When the cooling rate decreases, the atoms become packed more orderly and ultimately form a nano-polycrystalline structure dominated by FCC structures. The BCC structures appear only as an intermediate state acting on the course of crystallization, while the HCP structure can be viewed as the precursor of the malposed FCC structure due to the identical first neighbor distances. In liquid HEAs, the low-symmetry and low-coordination bond pairs, either transform to high-symmetry and high-coordination 1551 bond pairs, or transform to 1(5,4)41 bond pairs for FCC structure and 1661 bond pairs for an HCP structure, depending on the cooling rates. This study will contribute to a better understanding of the essential phase change in HEAs.