The Support Vector Machine (SVM), a known discriminative classifier is ineffective in dealing with imbalanced classification problems where the training examples of target class are outnumbered by non-target class examples. Though cost-SVM (cSVM) has been proposed to tackle the imbalanced datasets by assigning different cost functions to different classes, the performance is less than satisfactory due to its limited ability to enforce cost-sensitivity. In this research, a generative classifier, Gaussian Mixture Model (GMM) is studied which can learn the distribution of the imbalanced data to improve the discriminative power between imbalanced classes. By fusing this knowledge into cSVM, a model fusion approach, termed CSG (cSVM+GMM), is proposed to tackle the imbalanced classification problem. Experimental results on eleven benchmark datasets and one medical imaging dataset show the effectiveness of CSG in dealing with imbalanced classification problems.