In this paper, the model of a one-dimensional generalized Fibonacci quasi-periodical phononic crystal is firstly proposed, the transmission coefficients of the elastic waves through this 1D quasi-periodical phoninic crystal are numerically calculated, and the obtained transmission coefficients are compared with those of the phononic crystals with periodical structure and with normal Fibonacci structure. The results show that the band gap can also be found in the phononic crystals with the generalized Fibonacci quasi-periodical structure, and the frequency range of the gap is larger than that of both the periodical structure and the normal Fibonacci structure. However, there are more strongly localized resonant modes in the gap of the generalized Fibonacci quasi-periodical phononic crystals. This study to the localized modes is useful to the fabrication of the acoustic or elastic wave filters.