This study is devoted to extracting significant texture features from dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) of the breast using curvelet features and to classify breast masses into malignant and benign using the calculated features. The authors utilised the first generation of curvelet transform in the interpretation of breast tumours on DCE-MRI. The analysis is performed after injecting 23 patients with a contrast agent and 23 mass lesions were extracted from these patients. Then, 288 statistical parameters were extracted by calculating the mean and variance of the curvelet coefficients of tumour texture in sub-band images. Due to a large number of extracted features and the presence of redundant and inter-correlated descriptors, they used a combination of genetic algorithm (GA) and Pearson's correlation for feature selection and a three-layer artificial neural network (ANN) for classification of malignant and benign breast lesions. The GA-ANN model has yielded a good diagnostic accuracy (96%), sensitivity (92%) and specificity (100%). Also, the area under the receiver operating characteristic curve was 0.955. The curvelet transform was able to effectively quantify the distribution of contrast agent in tumour texture, which is different in malignant and benign tumours.