A novel no-reference (NR) image quality assessment (IQA) method is proposed for assessing image quality across multifarious distortion categories. The new method transforms distorted images into the shearlet domain using a non-subsample shearlet transform (NSST), and designs the image quality feature vector to describe images utilizing natural scenes statistical features: coefficient distribution, energy distribution and structural correlation (SC) across orientations and scales. The final image quality is achieved from distortion classification and regression models trained by a support vector machine (SVM). The experimental results on the LIVE2 IQA database indicate that the method can assess image quality effectively, and the extracted features are susceptive to the category and severity of distortion. Furthermore, our proposed method is database independent and has a higher correlation rate and lower root mean squared error (RMSE) with human perception than other high performance NR IQA methods.