Support Vector Machines (SVM) has been extensively studied and has shown remarkable success in many applications. However the success of SVM is very limited when it is applied to the problem of learning from imbalanced datasets in which negative instances heavily outnumber the positive instances (e.g. in medical diagnosis and detecting credit card fraud). In this paper, we propose the fuzzy asymmetric algorithm to augment SVMs to deal with imbalanced training-data problems, called FASVM, which is based on fuzzy memberships, combined with different error costs (DEC) algorithm. We compare the performance of our algorithm against these two algorithms, along with different error costs and regular SVM and show that our algorithm outperforms all of them.