Over the past couple of decades, numerous image quality assessment (IQA) algorithms have been developed to estimate the quality of images that contain a single type of distortion. Although in practice, images can be contaminated by multiple distortions, previous research on quality assessment of multiply-distorted images is very limited. In this paper, we propose an efficient algorithm to blindly assess the quality of both multiply and singly distorted images based on predicting the distortion parameters using a bag of natural scene statistics (NSS) features. Our method, called MUltiply- and Singlydistorted Image QUality Estimator (MUSIQUE), operates via three main stages. In the first stage, a two-layer classification model is employed to identify the distortion types (i.e., Gaussian blur, JPEG compression, and white noise) that may exist in an image. In the second stage, specific regression models are employed to predict the three distortion parameters (i.e., σG for Gaussian blur, Q for JPEG compression, and σN for white noise) by learning the different NSS features for different distortion types and combinations. In the final stage, the three estimated distortion parameter values are mapped and combined into an overall quality estimate based on quality-mapping curves and the most-apparent-distortion strategy. Experimental results tested on three multiply-distorted and seven singly-distorted image quality databases demonstrate that the proposed MUSIQUE algorithm can achieve better/competitive performance as compared to other state-of-the-art FR/NR IQA algorithms.