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By viewing the quasi-periodicity as the deviation from the periodicity in a particular way, the quasi phononic crystal that has quasi-periodicity (Fibonacci sequence) in one direction and translational symmetry in the other direction is considered. The band structures are characterized by localization factors which are calculated by using the plane-wave-based transfer-matrix method. The results show that the localization factor is an effective parameter in characterizing the band gaps of two-dimensional phononic crystals with one-dimensional quasi-periodicity. The quasi phononic crystals exhibit more band gaps with narrower width than the ordered and randomly disordered systems.