Synthetic aperture radar (SAR), due to its inherent characteristics, will produce speckle noise, which results in the deterioration of image quality, so the removal of speckle in SAR image is very important for the subsequent high-level image processing. In order to balance the relationship between denoising and texture preservation, we propose a multiscale residual dense dual attention network (MRDDANet) for SAR image denoising. This algorithm can effectively suppress the speckle while fully retaining the texture details of the image. In MRDDANet, shallow features are extracted from the noisy images by multiscale modules with different kernel sizes, and then, the extracted shallow features are mapped to the residual dense dual-attention network to obtain the deep features of SAR image. Finally, the final denoising image is generated through global residual learning. MRDDANet has advantages of both multiscale blocks and residual dense dual attention networks. The dense connection can fully extract features in the image, and the dual-channel attention enables MRDDANet to pay more attention to noise information, which is beneficial to remove noise and keep the details of the original image at the same time. Compared with state-of-the-art algorithms, the results of the experiment indicate that our method not only improves various objective indicators but also shows great advantages in visual effects.