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In this paper, directional adaptive red-black wavelet transform (DA-RBWT) is proposed. Instead of the conventional red-black wavelet transform (RBWT) for directional prediction with fewer directions, DA-RBWT use three or four pixel to adaptively predict the value of middle pixel according to the correlation among its neighboring pixels. Due to its adaptability to local image features, the DA-RBWT improves the directional prediction, especially for the regions of edges and textures. Experimental results show that the DA-RBWT is sparser for image representation than RBWT. In addition, the denoising application of DA-RBWT is examined. It is shown the proposed algorithm outperform the RBWT based denoising algorithm.