Although distinct growth behaviors on different faces of hexagonal ice have long been suggested, their understanding on a molecular scale has been hampered due to experimental difficulties near interfaces. We present a molecular dynamics simulation study to unravel the molecular origin of anisotropy in the growth kinetics of hexagonal ice by visualizing the formation of transient water structures in the growing ice interface. During ice growth, the formation of transient structures and their rearrangement to the final ice configuration are observed irrespective of growth direction. However, we find that their structure and duration differ significantly depending on growth direction. In the direction perpendicular to the basal face of hexagonal ice along which growth occurs most slowly, a two-dimensional transient structure, which is formed by competing hexagonal and cubic arrangements within the same layer, persists for a significant period of time, contrasted with short-lived transient structures in other directions. This observation of such transient water structures and their rearrangement during ice growth provides a clear explanation of different growth rates on each face of hexagonal ice on a molecular scale.