A novel image denoising algorithm based on undecimated dual-tree complex wavelet transform domain was proposed. Firstly, the dependency among the real and imaginary parts of undecimated dual-tree complex wavelet coefficients in the same direction was analyzed. According to the dependency characterization and empirical joint distribution of the original clean images, an elliptically contoured and anisoropic bivariate non-Gaussian statistical model was established to fit the empirical joint distribution of real and imaginary parts. Then the joint distribution as a prior model was modeled with an adaptive and anisoropic non-Gaussian bivariate statistical model as well as reflects the dependencies among coefficients. It finally uses a maximum posteriori probability from noise image to estimate the original image wavelet coefficients,so as to achieve the purpose of denoising. A denoising rule with the simple closed-form solution was derived from the model. The experimental results demonstrate that the proposed method can obtain better performances than other existing outstanding denoising algorithms in terms of peak signal-to-noise ratio and achieve a better visual quality. It also offers a better recovery of texture information compared to others.