The locally resonant phononic crystal (LRPC) composite double panel structure (DPS) made of a twodimensional periodic array of a two-component cylindrical LR pillar connected between the upper and lower composite plates is proposed. The plates are composed of two kinds of materials and periodically etched holes. In order to reveal the bandgap properties of structure theoretically, the band structures, displacement fields of eigenmodes and transmission power spectrums of corresponding 8 × 8 finite structure are calculated and displayed by using finite element method (FEM). Numerical results and further analysis demonstrate that if the excitation and response points are picked on different sides of the structure, a wide band gap with low starting frequency is opened, which can be treated as the coupling between dominant vibrations of pillars and plate modes. In addition, the influences of filled-in rubber, etched hole and viscidity of soft material on band gap are studied and understood with the help of “base-spring-mass” simplified model.