A new denoising algorithm using Fast Guided Filter and Discrete Wavelet Transform is proposed to remove Gaussian noise in an image. The Fast Guided Filter removes some part of the details in addition to noise. These details are estimated accurately and combined with the filtered image to get back the final denoised image. The proposed algorithm is compared with other existing filtering techniques such as Wiener filter, Non Local means filter and bilateral filter and it is observed that the performance of this algorithm is superior compared to the above mentioned Gaussian noise removal techniques. The resultant image obtained from this method is very good both from subjective and objective point of view. This algorithm has less computational complexity and preserves edges and other detail information in an image.