Many existing color image denoising methods process color channels individually and fail to consider their cross-channel correlations. To solve this problem, in this paper, we employ the quaternion representation of the color image and propose a novel Quaternion Non-local Total Variation (QNLTV) model to remove Gaussian noise from color images. We first introduce the coupled quaternion distance to measure the color image patch similarity. Decomposing the color image into brightness and chromaticity components in quaternion domain, we then divide the QNLTV model into two quaternion optimizaiton problems and solve them alternatively. Experiment results show that QNLTV has the significantly better denoising performance than competing methods in terms of visual and quantitative evaluations.