During acquisition, processing, compression and transmission, images may be corrupted by multiple distortions such as blur, noise or compression artefacts. However, most of the existing image quality assessment (IQA) methods are designed for images degraded by a single distortion type. This paper proposes a reduced-reference (RR) IQA method for quality assessment of multiply distorted images. The method extracts a number of quality-characterizing features from the reference and the distorted images for quality prediction. Based on internal generative mechanism (IGM) theory, the images are decomposed first into their predicted and disorderly portions. Next, a number of quality-characterizing features are extracted from each portion and feature differences are computed between the reference and distorted images. Finally, support vector regression (SVR) is adopted to obtain a quality score. Experimental results on public multiply-distorted image databases, namely MDID2015 and MLIVE, show that the proposed method is well-correlated with subjective ratings and outperforms several IQA methods.