The contourlet coefficients corresponding to an image have strong correlations both at the same scale and between neighboring scales. Therefore, an adaptive threshold is firstly constructed by the intra-scale correlation property of contourlet coefficients. After the adaptive thresholding denoising, the inter-scale correlation of the contourlet coefficients is utilized to decide what processed coefficients to use. Based on the two above correlation properties of contourlet coefficients, a new adaptive contourlet-domain image deniosing algorithm is thus presented. The new algorithm cannot only remove noise thoroughly, but maintain the edges of the image effectively. Experimental results show that the proposed algorithm can get better denoising results and is superior to the available methods both visually and objectively.