Fatty liver is a prevalent disease and is the major cause for the dysfunction of the liver. If fatty liver is untreated, it may progress into chronic diseases like cirrhosis, hepatocellular carcinoma, liver cancer, etc. Early and accurate detection of fatty liver is crucial to prevent the fatty liver progressing into chronic diseases. Based on the severity of fat, the liver is categorized into four classes, namely Normal, Grade I, Grade II and Grade III respectively. Ultrasound scanning is the widely used imaging modality for diagnosing the fatty liver. The ultrasonic texture of liver parenchyma is specific to the severity of fat present in the liver and hence we formulated the quantification of fatty liver as a texture discrimination problem. In this paper, we propose a novel algorithm to discriminate the texture of fatty liver based on curvelet transform and SVD. Initially, the texture image is decomposed into sub-band images with curvelet transform enhancing gradients and curves in the texture, then an absolute mean of the singular values are extracted from each curvelet decomposed image, and used it as a feature representation for the texture. Finally, a cubic SVM classifier is used to classify the texture based on the extracted features. Tested on a database of 1000 image textures with 250 image textures belonging to each class, the proposed algorithm gave an accuracy of 96.9% in classifying the four grades of fat in the liver.