Abstract: To reflect different intensities of noises among the different bands in the transform domain and the intrinsic structures of the transformed data, a new approach for denoising the hyperspectral images is proposed based on Principal Component Analysis (PCA) and dictionary learning. At first, a group of the principle component images are achieved by using the PCA transform. Then, these noises which exist in the spatial- and the spectral- domain of the components with low energy are denoised by an adaptively learned dictionary based sparse representation method and the dual-tree complex wavelet transform, respectively. Finally, the denoised data is obtained using the inverse PCA transform. By taking advantages of principal component analysis and dictionary learning, the proposed approach is superior to the traditional ones in preserving the details and alleviating the blocking artifacts. The experiment results on the synthetic and real hyperspectral remote sensing images demonstrate the effectiveness of the proposed approach.