We have performed ab initio molecular dynamics simulation of Ni62.5Nb37.5 alloy at descending temperatures (from 1800 to 300 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 amorphous states, and it becomes dominant in the amorphous states. Moreover, we demonstrated the existence of Ni-centered Ni7Nb6 icosahedral clusters as the major local structural unit in the Ni62.5Nb37.5 amorphous alloy. This finding agrees well with our previous "cluster-plus-glue-atom" model for the Ni-Nb bulk metallic glasses. The positions of the first peaks of Ni-Nb pair correlation functions are lower than the sum of the metallic radii of Ni and Nb, suggesting enhanced chemical bonding between Ni and Nb atoms in Ni62.5Nb37.5 alloy. Analysis of electronic structures further revealed that the Nb-to-Ni charge transfer is responsible for the enhanced Ni-Nb bonding.