Demosaicking and denoising are critical for deciding on digital camera performance. However, conventional joint demosaicking and denoising methods use traditional hand-crafted filters for preprocessing and image restoration. Therefore, it is susceptible to noise and can produce many artifacts for images with numerous edges. This paper proposes an end-to-end multi-level wavelet attention convolutional neural network (CNN) that improves image restoration performance by reducing false color artifacts, over-smoothing, and blurring during demosaicing and denoising. In detail, this paper proposes a CNN-based preprocessing method that learns the mosaic image's inter-color correlation, improving the edge's color restoration performance. Furthermore, this paper presents a multi-level feature extraction convolutional block using the Haar wavelet-based discrete wavelet transform (DWT) to remove noise from images and restore colors better at the same time. Therefore, it preserves the information of input image and feature maps, learns the correlation between global and local features, improves image restoration performance, and suppresses phenomena such as over-smoothing that tend to occur in DWT-based denoising. The proposed method is an end-to-end network structure with CNN-based preprocessing methods. In experimental results, the proposed method improves PSNR by 3.67 dB and 0.35 dB on average compared with the traditional methods and the CNN-based methods, respectively, for the dataset with many high-frequency components.