Salt-and-pepper (SAP) noise is one of the common impulse noises. It is generated mostly during the process of image capture and storage, due to false locations in memory and damaged image sensors. SAP noise seriously degrades the quality of images and affects the performance of subsequent image processing, such as edge detection, image segmentation and object recognition. Thus, it is quite necessary to remove SAP noise from corrupted images efficiently. In this paper, we propose a fast-adaptive Gaussian-weighted mean filter (FAGWMF) for removing salt-and-pepper noises. Our denoising filter consists of four stages. At the first stage, we preprocess the image by enlarging and flipping the image. Then, we detect noisy pixels by comparing the pixel value with the maximum (255) and minimum (0) value. One pixel is regarded as noise if its value is equal to the maximum or minimum value. Otherwise, it is regarded as noisefree pixel. At the third stage, we determine the working window size by enlarging the filter window continuously until the quantity of noise-free pixels it includes reaches to the predetermined threshold or the window radius reaches to the predetermined maximum value. At the last stage, we replace each noise candidate by its Gaussian-weighted mean value of the noise-free pixels in window. Using Gaussian-weighted template, the central candidates will get larger weights than those on edges, which helps to preserve the edge information efficiently. Simulation results show that compared to some state-of-the-art algorithms, our proposed filter has faster execution speed and better restoration quality.