Mixture noise removal is a fundamental problem in hyperspectral images' (HSIs) processing that holds significant practical importance for subsequent applications. This problem can be recast as an approximation issue of a low-rank matrix. In this paper, a novel smooth rank approximation (SRA) model is proposed to cope with these mixture noises for HSIs. The crux idea is to devise a general smooth function under some assumptions to directly approximate the rank function, which attempts to explore a closer approximation than conventional methods. This new optimization model can be easily solved by the convex analysis tool and can remove the mixture noises of HSIs quickly and effectively. Subsequently, we give a feasible iterative algorithm, and the corresponding convergence analysis is discussed mathematically. Experimental results from the simulated data set as well as real data sets illustrate that the proposed SRA method significantly outperforms the state-of-the-art methods on HSI denoising.