Recent years have witnessed the great success of deep convolutional neural networks (CNNs) in image denoising. Albeit deeper network and larger model capacity generally benefit performance, it remains a challenging practical issue to train a very deep image denoising network. Using multilevel wavelet-CNN (MWCNN) as an example, we empirically find that the denoising performance cannot be significantly improved by either increasing wavelet decomposition levels or increasing convolution layers within each level. To cope with this issue, this paper presents a multi-level wavelet residual network (MWRN) architecture as well as a progressive training (PTMWRN) scheme to improve image denoising performance. In contrast to MWCNN, our MWRN introduces several residual blocks after each level of discrete wavelet transform (DWT) and before inverse discrete wavelet transform (IDWT). For easing the training difficulty, scale-specific loss is applied to each level of MWRN by requiring the intermediate output to approximate the corresponding wavelet subbands of ground-truth clean image. To ensure the effectiveness of scale-specific loss, we also take the wavelet subbands of noisy image as the input to each scale of the encoder. Furthermore, progressive training scheme is adopted for better learning of MWRN by beigining with training the lowest level of MWRN and progressively training the upper levels to bring more fine details to denoising results. Experiments on both synthetic and real-world noisy images show that our PT-MWRN performs favorably against the state-of-the-art denoising methods in terms both quantitative metrics and visual quality.