The simplified model of locally resonant phononic crystal composite double panel structure is proposed based on the widely researched locally resonant phononic crystal plates, and an improved plane wave expansion method is applied to calculate the structure. Numerical results and further analyses demonstrate that a complete band gap is opened in the low frequency region. The torsional spring, size and viscidity of soft material have obvious effects on the band gap, which cannot be influenced by the rotational inertia. All the results are expected to be of theoretic significances and engineering application prospects in the field of vibration and noise reduction.