This paper presents a novel despeckling algorithm that can be used to enhance image quality in medical ultrasound images. Firstly, the log-transformed images are transformed by dual-tree complex wavelet transform (DTCWT). And then, we use a non-Gaussian statistical model with an adaptive smoothing parameter for ideal image signal in the transformed domain. According to Bayesian theory, the MAP estimator is obtained with a proposed adaptive threshold which has better despeckling performance by exploiting the interscale properties of wavelet coefficients. The proposed approach results in significant speckle reduction and preserve details of ultrasound images at the same time while the introduced distortions are not noticeable.