X-ray computed tomography (CT) is a mainstream medical imaging modality. The widespread use of CT has made image denoising of low-dose CT (LDCT) images a key issue in medical imaging. Deep learning (DL) methods have been successful in this area over the past few years, but most DL-based dual-domain methods directly filter the sinogram domain data, which is prone to induce new artifacts in the reconstructed image. This paper proposes a new method called DD-WGAN, which has an image domain generator network (IDG-Net) and two discriminator networks, namely the image domain discriminator network (ID-Net) and the sinogram domain discriminator network (SD-Net). We use dual-domain discriminators to balance the data weights of sinogram and image. Experimental results show that the proposed method achieves significantly improved LDCT denoising performance.