Recently, a noncentrosymmetric crystal, KNaNbOF5, has attracted attention due to its potential to present piezoelectric properties. Although α- and β-KNaNbOF5 are similar in their stoichiometries, their structural frameworks, and their synthetic routes, the two phases exhibit very different properties. This paper presents, from first-principles calculations, comparative studies of the structural, electronic, piezoelectric, and elastic properties of the α and the β phase of the material. Based on the Christoffel equation, the slowness surface of the acoustic waves is obtained to describe its acoustic prosperities. These results may benefit further applications of KNaNbOF5.