Abstract: The unit cell of the one-dimensional phononic crystal is reduced to a spring-mass structure with limited number of degrees. The lattice vibrations are investigated under the dual variable system, and the dispersion relation is obtained by the symplectic mathematical method. Furthermore, the eigenfrequency is given by using the Wittrick-Williams algorithm, thus the band gap is obtained. Comparing the results calculated by the present method with the traditional lump-mass method, it is obvious that there is a good agreement. However, the former is capable of improving the calculation accuracy and computational efficiency, and more importantly, having better convergence.