Ground-penetrating radar (GPR), as a non-invasive instrument, has been widely used in civil engineering. In GPR B-scan images, there may exist random noise due to the influence of the environment and equipment hardware, which complicates the interpretability of the useful information. Many methods have been proposed to eliminate or suppress the random noise. However, the existing methods have an unsatisfactory denoising effect when the image is severely contaminated by random noise. This paper proposes a multi-scale convolutional autoencoder (MCAE) to denoise GPR data. At the same time, to solve the problem of training dataset insufficiency, we designed the data augmentation strategy, Wasserstein generative adversarial network (WGAN), to increase the training dataset of MCAE. Experimental results conducted on both simulated, generated, and field datasets demonstrated that the proposed scheme has promising performance for image denoising. In terms of three indexes: the peak signal-to-noise ratio (PSNR), the time cost, and the structural similarity index (SSIM), the proposed scheme can achieve better performance of random noise suppression compared with the state-of-the-art competing methods (e.g., CAE, BM3D, WNNM).