Gamut mapping is a key technology for color image transmission and reproduction in different devices, and it is also the core part of modern color management system. However, there are few studies on the quality evaluation of gamut mapping images, therefore, in this paper, a no-reference quality evaluation algorithm based on natural scene statistics for gamut mapping images is proposed. First, the gamut mapping images are converted to the Spatial-CIELAB color space and the three attributes (e.g., luminance, chroma and hue) are extracted. Next, luminance components are decomposed by using Log-Gabor filter, and statistical features are extracted in the frequency domain to characterize image structure distortion and contrast distortion. For the two components of chroma and hue, statistical features are extracted in the spatial domain to characterize color distortion. Then, combined with subjective scores and extracted features, the backward propagation neural network is used to train the image quality prediction model. Finally, this model is employed to assess the image quality. The experimental results prove that the proposed method is superior to the existing no-reference quality evaluation algorithms.