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In this paper, we propose a novel full-reference objective quality assessment metric for screen content images (SCIs) by structure features and uncertainty weighting (SFUW). The input SCI is first divided into textual and pictorial regions. The visual quality of textual regions is estimated based on perceptual structural similarity, where the gradient information is adopted as the structural feature. To predict the visual quality of pictorial regions in SCIs, we extract the structural features and luminance features for similarity computation between the reference and distorted pictorial patches. To obtain the final visual quality of SCI, we design an uncertainty weighting method by perceptual theories to fuse the visual quality of textual and pictorial regions effectively. Experimental results show that the proposed SFUW can obtain better performance of visual quality prediction for SCIs than other existing ones.