The energy band characteristic of two-dimensional ternary lattice tungsten-silicone rubber phononic crystals was analyzed by both the plane wave expansion method and finite element method. The propagation characteristics of elastic wave in a silicone rubber plate were analyzed, which were embedded with periodically arranged cylindrical tungsten blocks of the same pore size. Moreover, the special phenomena in the band structure were also discussed, such as the Dirac point and the degeneracy near the Dirac point and so on. The three-dimensional energy band diagram and the main deformation under different modes were given. It is found that stress concentration easily occur in the combination part of the periodic composite material. Then the influence of different material parameters on the bandgap were studied and the initial frequency of the first complete bandgap gradually increases with the increase of the density ratio (the ratio of the scatterer density to the matrix density). However, the bandwidth decreases gradually since the cutoff frequency changes little. Compared with Young's modulus, density has more influence on the bandgap of the periodic composite material. The results of this paper could provide some theoretical guidance for practical engineering application.