We have performed ab initio molecular dynamics simulation of Cu64Zr36 alloy at descending temperatures (from 2000 K to 400 K) and discussed the evolution of short-range order with temperature. The pair-correlation functions, coordination numbers, and chemical compositions of the most abundant local clusters have been analyzed. We found that icosahedral short-range order exists in the liquid, undercooled, and glass states, and it becomes dominant in the glass states. Moreover, we demonstrated the existence of Cu-centered Cu8Zr5 icosahedral clusters as the major local structural unit in the Cu64Zr36 amorphous alloy. This finding agrees well with our previous cluster model of Cu-Zr-based BMG as well as experimental evidences from synchrotron x ray and neutron diffraction measurements.