The fragility of materials should be related to a local structure formed in supercooled liquid states. Especially, in the cases of metallic glasses, the icosahedral order formation is considered to play an important role. To clarify the relation between the local structure formation and the relaxation behavior (or fragility) in the supercooled liquid states of metallic glasses, molecular dynamics simulations were performed for a simple model of binary alloys, in which we can change the atomic size ratio. From the simulation results, we found that the icosahedral clusters exist in supercooled liquid states and form a medium-range network structure in strongly supercooled regime near the glass transition as well as in the glassy states. We also found that the number density of the clusters increases as the atomic size difference increases. Consequently, the calculated fragility parameter takes a lower value in a system with larger atomic size difference due to the richness of the icosahedral clusters.