Discriminative learning-based image denoisers have achieved promising performance on synthetic noises such as Additive White Gaussian Noise (AWGN). The synthetic noises adopted in most previous work are pixel-independent, but real noises are mostly spatially/channel-correlated and spatially/channel-variant. This domain gap yields unsatisfied performance on images with real noises if the model is only trained with AWGN. In this paper, we propose a novel approach to boost the performance of a real image denoiser which is trained only with synthetic pixel-independent noise data dominated by AWGN. First, we train a deep model that consists of a noise estimator and a denoiser with mixed AWGN and Random Value Impulse Noise (RVIN). We then investigate Pixel-shuffle Down-sampling (PD) strategy to adapt the trained model to real noises. Extensive experiments demonstrate the effectiveness and generalization of the proposed approach. Notably, our method achieves state-of-the-art performance on real sRGB images in the DND benchmark among models trained with synthetic noises. Codes are available at https://github.com/yzhouas/PD-Denoising-pytorch.