The near-field acoustic holography is an acoustic image method, which can be used to localize sound source effectively in technical practice. The equivalent source method can be applied to fix the ℓ2 norm regularized inverse problem and the ℓ1 norm regularized inverse problem for different numerical models of sound sources. To enhance the resolution quality of traditional ESM and narrow the sidelobe, we propose an improved fast iterative shrinkage / thresholding algorithm for sound source identification, which is based on the equivalent source method (mIFISTESM-v). This method is a combined application of the modified improved fast iterative shrinkage thresholding equivalent source method and functional beamforming. Its practicability is evaluated by the numerical simulation of the resolution quality analysis, and the experiments of the single sound source location and the coherent sound source location. Results show that the proposed method can achieve excellent sound source identification and location, and the main lobe area obtained by this method is smaller than 0. 002.