Anatomical and biophysical modeling of left atrium (LA) and proximal pulmonary veins (PPVs) is important for clinical management of several cardiac diseases. Magnetic resonance imaging (MRI) allows qualitative assessment of LA and PPVs through visualization. However, there is a strong need for an advanced image segmentation method to be applied to cardiac MRI for quantitative analysis of LA and PPVs. In this study, we address this unmet clinical need by exploring a new deep learning-based segmentation strategy for quantification of LA and PPVs with high accuracy and heightened efficiency. Our approach is based on a multi-view convolutional neural network (CNN) with an adaptive fusion strategy and a new loss function that allows fast and more accurate convergence of the backpropagation based optimization. After training our network from scratch by using more than 60K 2D MRI images (slices), we have evaluated our segmentation strategy to the STACOM 2013 cardiac segmentation challenge benchmark. Qualitative and quantitative evaluations, obtained from the segmentation challenge, indicate that the proposed method achieved the state-of-the-art sensitivity (90%), specificity (99%), precision (94%), and efficiency levels (10s in GPU, and 7.5 min in CPU).