We have proposed and demonstrated a double-cladding fiber (DCF) with cladding-mode resonance property for broadband acoustic vibration sensing. Since the fundamental mode in the core waveguide is able to be coupled to LP05 mode in the tube waveguide once the phase-matching condition is fulfilled, the transmission spectrum can exhibit a dip with a large extinction ratio. an acoustic vibration could induce the wavelength shift of such transmission spectrum, so that the intensity variation at a wavelength near the dip is coded with the information of the acoustic vibration signal. By demodulating the response of intensity variation, the frequency of the applied acoustic vibration signal can be recovered. Such a DCF-based sensor with an intensity modulation could measure the acoustic vibration with a broadband frequency range from 1 Hz to 400 kHz and exhibits the maximum signal-to-noise ratio (SNR) of ~80.79 dB when the vibration frequency is 20 kHz. The obtained results show that the proposed DCF-based acoustic vibration sensor has a potential application in environmental assessment, structural damage detection, and health monitoring.