The first fluorooxoborate with reversible phase transition, BaB4O5F4, has been obtained. Interestingly, the two polymorphs, α- and β-BaB4O5F4 with rare [BOF3], feature various one-dimensional chains composed of the unprecedented fundamental building blocks of [B16O21F16] and [B4O6F4], respectively. First-principles calculations were performed to elucidate the structure-property relationships.