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In this paper, we propose a new wavelet shrinkage algorithm based on fuzzy logic. Fuzzy logic is used for taking neighbor dependency and uncorrelated nature of noise into account in wavelet-based image denoising. For this reason, we use a fuzzy feature for enhancing wavelet coefficients information in the shrinkage step. Then a fuzzy membership function shrinks wavelet coefficients based on the fuzzy feature. We examine our image denoising algorithm in the dual-tree discrete wavelet transform, which is the new shiftable and modified version of discrete wavelet transform. Extensive comparisons with the state-of-the-art image denoising algorithm indicate that our image denoising algorithm has a better performance in noise suppression and edge preservation.