© 2019 IEEE. Cardiac magnetic resonance imaging provides a way for heart's functional analysis. Through segmentation of the left ventricle from cardiac cine images, physiological parameters can be obtained. However, manual segmentation of the left ventricle requires significant time and effort. Therefore, automated segmentation of the left ventricle is the desired and practical alternative. This paper introduces a novel framework for the automated segmentation of the epi- and endo-cardial walls of the left ventricle, directly from the cardiac images using a fully convolutional neural network similar to the U-net. There is an acute class imbalance in cardiac images because left ventricle tissues comprise a very small proportion of the images. This imbalance negatively affects the learning process of the network by making it biased toward the majority class. To overcome the class imbalance problem, we propose a novel loss function into our framework, instead of the traditional binary cross entropy loss that causes learning bias in the model. Our new loss maximizes the overall accuracy while penalizing the learning bias caused by binary cross entropy. Our method obtained promising segmentation accuracies for the epi- and endo-cardial walls (Dice 0.94 and 0.96, respectively) compared with the traditional loss (Dice 0.89 and 0.87, respectively)