Due to the limitation of sensors and atmospheric conditions, hyperspectral images (HSI) are always contaminated by heavy noises, which significantly limits the subsequent applications. To mitigate the problem, this paper proposes a novel subspace spatial-spectral low rank learning method for hyper-spectral denoising. It is based on the assumption that spectra in HSI lie in a low-rank subspace and nonlocal spatial patches are self-similar. The spectral low-rank property is explored by decomposing the clean HSI into two sub-matrices of low rank and the spatial self similarity is exploited by weighed nuclear norm minimization in a nonlocal sense. The proposed restoration model is formulated into an iterative optimization model which can be effectively solved by a cyclic descent algorithm. Experimental results on both simulated and real HSI datasets show that the proposed method can significantly outperform the state-of-the-art methods in terms of quantitative assessment and visual quality.