It is always an issue for researchers to control the propagation of sound wave at will. A kind of acoustic metamaterial built with artificial microunits attracts the attention of researchers, because it possesses many unique properties that cannot be realized by natural materials, such as negative refractive index, slab focusing, and cloak. The Doppler effect leads to the frequency change of a wave because of the relative motion between the observer and the source. In 1968, Veselago[Veselago V G 1968 Soviet Physics Uspekhi 10 509] theoretically proposed that a metamaterial with a negative refraction can result in an inverse Doppler effect. The investigation of inverse Doppler effect has been developed with the improvement of metamaterials. However, the design methods of these metamaterials generally need ideal material parameters, which are difficult to obtain experimentally. Besides, although the inverse Doppler effects are realized by some electromagnetic metamaterials in optical and microwave frequencies, the relevant researches in acoustic metamaterials make slow progress. In this work, a 2D acoustic metamaterial with negative mass density is fabricated. Our previous work has demonstrated that the air in the internal cavity of the unit cell will vibrate back and forth to generate the vibration velocity when the air is driven by a sound source. As the source frequency reaches the resonant frequency, large amounts of energy will be stored in the internal cavity. This accumulation of energy will cause the acceleration of the air in opposite direction to the sound pressure, thus this metamaterial will exhibit negative mass density. In this case, the direction of the phase velocity is exactly opposite to that of the group velocity of the sound wave. Therefore, the inverse Doppler effect of sound wave can be realized by this metamaterial. Since the unit cells with different lengths have different resonant frequencies and there is only weak interaction among the adjacent unit cells, the frequency band of the metamaterial with negative mass density can be broaden by combining several different unit cells. Our previous experiments have demonstrated that the mass density and refractive index of this metamaterial are negative over a broad frequency range from 1560 Hz to 5580 Hz and 1500 Hz to 5480 Hz, respectively. A testing equipment is constructed to measure the Doppler effect of this metamaterial from 1200 Hz to 6500 Hz. The experimental results show that when the sound source witha frequency of 2000 Hz approaches to the detector, the detected frequency is 1999.27 Hz, which is 0.73 Hz smaller than the source frequency; when the sound source recedes from the detector, the detected frequency is 2000.68 Hz, which is 0.68 Hz larger than the source frequency. Therefore, the inverse Doppler effect appears at 2000 Hz. The experimental results within the whole frequency range of negative refractive index show broadband inverse Doppler phenomena.