Hyperspectral images (HSIs) are often degraded by a mixture of various kinds of noise in the acquisition process, which can include Gaussian noise, impulse noise, dead lines, stripes, and so on. This paper introduces a new HSI restoration method based on low-rank matrix recovery (LRMR), which can simultaneously remove the Gaussian noise, impulse noise, dead lines, and stripes. By lexicographically ordering a patch of the HSI into a 2-D matrix, the low-rank property of the hyperspectral imagery is explored, which suggests that a clean HSI patch can be regarded as a low-rank matrix. We then formulate the HSI restoration problem into an LRMR framework. To further remove the mixed noise, the "Go Decomposition" algorithm is applied to solve the LRMR problem. Several experiments were conducted in both simulated and real data conditions to verify the performance of the proposed LRMR-based HSI restoration method.