The distributed state of noise existing among different bands of hyperspectral remote sensing image is complex, so the traditional denoising methods are hard to achieve the desired effect. In order to solve this problem, based on Principal Component Analysis (PCA), a novel denoising method for hyperspectral data was proposed combining with noise estimation and dictionary learning. Firstly, a group of the principal component images were achieved from the original hyperspectral data by using the PCA transform, which were divided into clear image group and noisy image group according to the corresponding energy. Then, according to any band image from noisy hyperspectral data, the noise standard deviation of the image was estimated via a noise estimation method based on Singular Value Decomposition (SVD). Meanwhile, combining this noise estimation method with denoising method via K-SVD dictionary learning, a new dictionary learning denoising method with adaptive noise estimation characteristics was proposed and applied to denoise those images from noisy image group with low energy where noise mainly existed. Finally, the final denoising image was obtained by weighted fusion according to the corresponding energy of each principal component image. The experimental results on simulated and real hyperspectral remote sensing data show that, compared with PCA, PCA-Bish and PCA-Contourlet, the Peak Signal-to-Noise Ratio (PSNR) of the image denoised by the proposed algorithm is improved by 1-3 dB, and more detailed information and better visual effect of the denoised image by the proposed method are achieved.