Infrared small target denoising is widely used in military and civilian fields. Existing deep learning-based methods are specially designed for optical images and tend to over-smooth the informative image details， thus losing the response of small targets. To both denoise and maintain informative image details， this paper proposes a gradient-aware channel attention network （GCAN） for infrared small target image denoising before detection. Specifically， we use an encoder-decoder network to remove the additive noise of the infrared images. Then， a gradient-aware channel attention module is designed to adaptively enhance the informative high-gradient image channel. The informative target region with high-gradient can be maintained in this way. After that， we develop a large dataset with 3981 noisy infrared images. Experimental results show that our proposed GCAN can both effectively remove the additive noise and maintain the informative target region. Additional experiments of infrared small target detection further verify the effectiveness of our method.