Speckle noise is a major shortcoming of any type of ultrasound imaging. Hence, speckle reduction is vital in providing a better clinical diagnosis. The key objective of any speckle reduction algorithm is to attain a speckle free image, whilst preserving the important anatomical features. In this paper, we introduce a nonlinear multi-scale complex wavelet diffusion based algorithm for speckle reduction and sharp edge preservation of 2D ultrasound images. The proposed method exploits some useful features of the dual tree complex wavelet transform and nonlinear diffusion. Simulated experimental results demonstrate that our proposed algorithm significantly reduces speckle noise while preserving sharp edges without discernible distortions. The proposed approach performs better than the previous existing approaches in both qualitative and quantitative measures.