Acoustic source imaging has nowadays been widely used in source localization and separation. In this paper, based on the deconvolution methods (DAMAS), we propose a robust super-resolution approach with sparsity constraint (SC-RDAMAS) to estimate both the positions and powers of the sources, as well as the noise variance in low Signal to Noise Ratio (SNR) situation. For effectively applying sparsity constraint, we explore a better initialization of source number to determine the bound of total source powers. By simulations and real data, we show that our SC-RDAMAS can obtain more accurate estimations of source positions and averaging powers, and can be more robust to strong noise interference, by comparison with the state of the art methods: the Beamforming, DAMAS, DAMAS with sparsity constraint (SC-DAMAS) and the Covariance Matrix Fitting (CMF) method. Indeed the computation burden of the proposed method is much lower than the CMF, so that our SC-RDAMAS is more applicable to scan the large region with super resolutions.