Most of the existing acoustic imaging studies in reverberant field ignore the influence of signal-to-noise ratio. As a result, commonly used beamforming algorithms in reverberant backgrounds have poor imaging accuracy for low signal-to-noise ratio sound sources. In response to that problem, an improved adaptive beamforming algorithm called SC-DAMAS is put forward in this paper. The algorithm replaces the free-field Green's function with the impulse response function, making the algorithm more suitable for acoustic imaging of low signal-to-noise ratio in a reverberant environment. Besides, the comparative simulation results with the conventional beamforming method and orthogonal matching pursuit algorithm-based DAMAS, as well as sound source acoustic imaging experiments are carried out to analyze its effectiveness. It is indicated that, in the reverberation field, the SC-DAMAS has no obvious sidelobes and achieves higher positioning accuracy for acoustic imaging of low signal-to-noise ratio sound source than the abovementioned counterparts, and its imaging test result is consistent with the actual situation, which verifies the effectiveness of the algorithm.