The work aims to effectively remove the salt and pepper noise in the image and improve the image quality. Separable dictionary and low-rank representation were combined to propose a sparse and low-rank representation with separable dictionary for image denoising (SLRR-SD). Firstly, the traditional overcomplete dictionary was replaced by a separable dictionary, which could directly represent two-dimensional images. Secondly, the Frobenius norm was used to separate dictionary constraints to mine the low-rankness inside the dictionary. In addition, in order to mine the sparse structure inside the image, the effectiveness of the representation was further improved by sparse constraints on the representation coefficients. The mean values of PSNR and FSIM of the proposed algorithm at 5%, 10%, 20% and 30% noise intensity were 32.736/0.975, 29.769/0.957, 29.295/0.951 and 26.768/0.921, respectively. The algorithm proposed preserves the correlation between adjacent columns. The optimization process of separable dictionary also reduces the computational burden. The experimental results show that the algorithm can better complete the denoising task while retaining the original image information.