The stubbed-on locally resonant (LR) phononic crystal double panel structure made of a two-dimensional periodic array of a cylindrical LR pillar connected between the upper and lower plates is constructed, and the bandgap properties of the structure are investigated in detail. The band structures, displacement fields of eigenmodes and transmission power spectrums of the corresponding finite structure are calculated by a finite element method. Numerical results and the further analysis demonstrate that a band gap with a low starting frequency and a wide band width is opened by the coupling between dominant vibrations of the pillars and plate modes, if the vibration source and receiver are considered on different sides of the structure. In addition, the influence of coupling between sound and vibration in the cavity on the band gap can be ignored. Many common characteristics are displayed between the double panel and the corresponding single plate, but the double panel structure has the excellent property of wide band gap. By changing the relevant parameters of the structure, the band gap can be adjusted effectively.