The damage monitoring methods in aircraft strength tests are based on manual inspection, and nondestructive testing and health monitoring are used to monitor the status of the test process. These methods have the disadvantages of low monitoring efficiency and high sensor installation requirements. Structural damage or damage precursors have a short-term impulsive behavior, and thus, this paper proposes an acoustic-based monitoring method, which combines microphone arrays and acoustic imaging algorithms for abnormal sound localization. Experimental validation and application are carried out on the composite material tensile fracture test and full-scale load carrying capacity test, and the conventional beamforming with diagonal removal (CBF-DR) algorithm and the orthogonal matching pursuit with singular value decomposition (OMP-SVD) algorithm are studied. The experimental results show the proposed acoustic-based method can monitor the short-term impulsive sound that characterizes the fracture and tearing, accurately capturing the structural response in the complex reverberant aircraft strength test environment. The OMP-SVD algorithm is rarely affected by the main lobe width and side lobe levels in different frequency ranges compared with the CBF-DR algorithm. It has better localization performance for multiple and reflected abnormal sound sources with different intensities.