The existing Gaussian-impulse mixed noise removal algorithms usually restore the noisy images via regularization technique by solving an optimal objective function iteratively, which results in low executive efficiency and limits their practical applications. To this end, in this paper we propose an image quality-aware fast blind denoising algorithm (IQA-FBDA), which takes convolutional neural network (CNN) as the core technique for the removal of Gaussian-impulse mixed noise. In the training phase, a shallow CNN-based image quality estimation model is first exploited to estimate the image quality of the image to be denoised. Then, according to the statistical distribution of the image qualities of a large number of noisy images, we construct a mixed noise pattern classification dictionary (MNPCD). Based on the MNPCD, the training noisy images are classified into 16 sub-classes, and then deep CNN-based denoisers for each class are trained. In the denoising phase, the image quality estimation model is first used to estimate the quality value of a given noisy image. After querying the quality value in the MNPCD, the corresponding pre-trained denoiser is exploited to achieve efficient blind image denoising. Experiments show that, compared with the state-of-the-art Gaussian-impulse mixed noise removal algorithms, the proposed one achieves comparable noise reduction effect with great improvement in terms of the execution efficiency, which makes it more practical.