Images may be corrupted by noise during the process of acquisition and transmission. The wavelet thresholding method has been demonstrated to be a powerful approach for noise reduction. This paper presents a novel wavelet thresholding procedure to suppress the additive Gaussian noises in images. The method overcomes the discontinuity of using a hard thresholding function and reduces the constant bias of using a soft thresholding function. The experimental results show that the proposed denoising method outperforms standard wavelet denoising techniques, i.e., soft thresholding and hard thresholding, in addition to other existing improved methods, i.e., hyperbolic thresholding and exponential thresholding, in terms of the PSNR (peak signal to noise ratio), SNR (signal to noise ratio), MSE (mean-squared error) and Image Histogram, making it suitable for significantly improving image quality.