Acoustic beamforming consists in measuring the sound field by the microphone array and infers the source strength in conjunction with the propagation model. A fundamental limitation of acoustic beamforming is determined by the aperture size of the array and the microphone density. In order to extend the working frequency range of conventional phased array beamforming, the sound sources are scanned by moving sequentially a small prototype array, resulting in a large array and high microphone density measurements, which is referred to as non-synchronous measurements beamforming. The main issue of nonsynchronous measurements beamforming is that the phase relationships between consecutive snapshots of non-synchronous measurements are missing and result in missing entries in the spectral matrix, however, complete spectral matrix information is crucial for high quality image of beamforming. Thus, non-synchronous measurements beamforming boils down to a spectral matrix completion problem which is modeled by a structured low rank model and solved by designed fast iteration algorithm. In particular, the structured low rank model is constructed by two ingredients: (1) the low rank property of the spectral matrix and (2) the continuity of the acoustic field. The simulation results show the nonsynchronous measurements beamforming extended the working frequency range of given small phased array from 2−2.8 kHz to 1.6−4.5 kHz with only 9 times non-synchronous measurements.