In this paper, a new measure for no-reference assessment of image quality based on the use of the structural properties of an image is proposed. As a measure, it is proposed to use the estimate of the Weibull distribution shape parameter, obtained by the set of image gradient magnitudes. This measure was previously successfully used to estimate the blurriness of the image. To test the effectiveness of the proposed measure, we used the data from the well-known TID2013 image database, which includes images of various types of distortions and corresponding mean opinion scores of the humans. The ability of the proposed measure is shown to distinguish the types of image distortions, which change the structural properties of an image.