The propagation of the elastic waves in one-dimensional (1D) solid–fluid quasi-periodic phononic crystals is studied by employing the concept of the localization factor, which is calculated by the transfer matrix method. The solid–fluid interaction effect at the interfaces between the solid and the fluid components is considered. For comparison, the periodic systems and aperiodic Thue–Morse sequence are also analyzed in this paper. The splitting phenomenon of the pass bands and bandgaps are discussed for these 1D solid–fluid systems. At last the influences of the material impedance ratios on the band structures of the 1D solid–fluid quasi-periodic phononic crystals arranged as Fibonacci sequence are discussed.