Deep learning has become a prominent tool for video denoising. However, most existing deep video denoising methods require supervised training using noise-free videos. Collecting noise-free videos can be costly and challenging in many applications. Therefore, this paper aims to develop an unsupervised deep learning method for video denoising that only uses a single test noisy video for training. To achieve this, an unsupervised loss function is presented that provides an unbiased estimator of its supervised counterpart defined on noise-free video. Additionally, a temporal attention mechanism is proposed to exploit redundancy among frames. The experiments on video denoising demonstrate that the proposed unsupervised method outperforms existing unsupervised methods and remains competitive against recent supervised deep learning methods.