Hyperspectral Image (HSI) always suffers from various noises such as Gaussian noise, impulse, stripe noise, etc. To ensure the performance of subsequent applications, a new method for HSI restoration was proposed based on weighted Schatten norm Low-Rank Representation (LRR). The proposed method introduced the LRR model into the HSI restoration. It can accurately approximate rank using the weighted Schatten norm instead of the nuclear norm. Furthermore, the initial noiseless image was utilized as the dictionary for LRR to improve the restoration ability. Then, the Laplacian regularizer was used to describe the intrinsic geometric information of the data and to protect details of the HSI. Experimental results on synthetic and real HSI data demonstrated that the proposed method achieves better visual quality and quantitative indices than several existing related methods. Compared with the classical restoration method based on low-rank priori, the mean peak signal-to-noise ratio and structural similarity indices of this algorithm increased by 2.74 dB and 0.03 respectively, and the mean spectral angle was reduced by 1.40. The new method not only takes advantage of the low-rank prior information in the spatial domain, but also keeps the intrinsic geometric structures in data, which helps restore quality clean images.