It is an important task to faithfully evaluate the perceptual quality of output images in many applications such as image compression, image restoration and multimedia streaming. A good image quality assessment (IQA) model should not only deliver high quality prediction accuracy but also be computationally efficient. The efficiency of IQA metrics is becoming particularly important due to the increasing proliferation of high-volume visual data in high-speed networks. We present a new effective and efficient IQA model, called gradient magnitude similarity deviation (GMSD). The image gradients are sensitive to image distortions, while different local structures in a distorted image suffer different degrees of degradations. This motivates us to explore the use of global variation of gradient based local quality map for overall image quality prediction. We find that the pixel-wise gradient magnitude similarity (GMS) between the reference and distorted images combined with a novel pooling strategy the standard deviation of the GMS map can predict accurately perceptual image quality. The resulting GMSD algorithm is much faster than most state-of-the-art IQA methods, and delivers highly competitive prediction accuracy.