A new nesting complex structure was designed to fabricate the one-dimensional phononic crystal. The transmissivity spectrograms of the longitudinal and transverse waves through the phononic crystal have been numerical calculated by using the transfer matrix method. The results show that the band gaps of the new phononic crystal are several times larger than that of the traditional one dimensional phononic crystal, and the local modes are present in the band gaps. We find the most effective factors to produce the huge band gaps and to influence the local modes. The features of the local modes depend strongly on the thickness and location of the impurity, which can extend the filter range of the phononic crystal to a lower frequency area. The mechanisms such as quasi-defects coupling and defects resonance are presented to explicate the results.