This paper presents a two-stage denoising method for hyperspectral image (HSI) by combining kernel principal component analysis (KPCA) and total variation (TV). In the first stage, we use KPCA denoising to reduce spectrally uncorrelated noise. In the second stage, the information content is largely separated from the remaining noise by means of principal component analysis (PCA). The remaining noise is then efficiently removed by fast primal-dual TV denoising in lowenergy PCA channels. Experimental results on simulated and real HSIs are very encouraging.