In this paper, we present one approach to improve the soundproofing performance of the double-panel structure (DPS) in the entire audible frequencies, in which two kinds of local resonances, the breathing-type resonance and the Helmholtz resonance, are combined. The thin ring resonator row and slit-type resonator (Helmholtz resonator) row are inserted between two panels of DPS together. Overlapping of the band gaps due to the individual resonances gives a wide and high band gap of sound transmission in the low frequency range. At the same time, the Bragg-type band gap is created by the structural periodicity of the scatterers in the high audible frequency range. In addition, the number of scatterer rows and the filling factor are investigated with regard to the sound insulation of DPS with sonic crystals (SCs). Consequently, the hybrid SC has the potential of increasing the soundproofing performance of DPS in the audible frequency range above 1 kHz by about 15 dB on average compared to DPS filled only with glass wool between two panels, while decreasing the total thickness and mass compared to the counterparts with the other type of local resonant sonic crystal.