Optical coherence tomography (OCT) is widely used for biomedical imaging and clinical diagnosis. However, speckle noise is a key factor affecting OCT image quality. Here, we developed a custom generative adversarial network (GAN) to denoise OCT images. A speckle-modulating OCT (SM-OCT) was built to generate low speckle images to be used as the ground truth. In total, 210 000 SM-OCT images were used for training and validating the neural network model, which we call SM-GAN. The performance of the SM-GAN method was further demonstrated using online benchmark retinal images, 3D OCT images acquired from human fingers and OCT videos of a beating fruit fly heart. The denoise performance of the SM-GAN model was compared to traditional OCT denoising methods and other state-of-the-art deep learning based denoise networks. We conclude that the SM-GAN model presented here can effectively reduce speckle noise in OCT images and videos while maintaining spatial and temporal resolutions.