Near-field aeroacoustic imaging has been the focus of great attentions of researchers and engineers in aeroacoustic source localization and power estimation for decades. Recently the deconvolution and regularization methods have greatly improved spatial resolution of the beamforming methods. But neither are they robust to background noises in the low Signal-to-Noise Ratio (SNR) situation, nor do they provide a wide dynamic range of power estimation. In this paper, we first propose an improved forward model of aeroacoustic power propagation, in which, we consider background noises and forward model uncertainty for the robustness. To solve the inverse problem, we then propose a robust Bayesian super-resolution approach via sparsity enforcing a priori. The sparse prior of source powers can be modeled by double exponential distribution, which can improve the spatial resolution and promote wide dynamic range of source powers. Both the hyperparameters and source powers can be alternatively estimated by the Bayesian inference approach based on the joint Maximum A Priori optimization. Finally our Bayesian approach is compared with some of the state-of-the-art methods on simulated, real and hybrid data. The main advantages of our approach are of robustness to noise, a wide dynamic range, super spatial resolution, and non-necessity for prior knowledge of the source number or SNR. It is feasible to apply it for aeroacoustic imaging with the 2D non-uniform microphone array in wind tunnel tests, especially for near-field monopole and extended source imaging.