Deep neural networks have achieved significant success for image recognition problems. Despite the wide success, recent experiments demonstrated that neural networks are sensitive to small input perturbations, or adversarial noise. The lack of robustness is intuitively undesirable and limits neural networks applications in adversarial settings, and for image search and retrieval problems. Current approaches consider augmenting training dataset using adversarial examples to improve robustness. However, when using data augmentation, the model fails to anticipate changes in an adversary. In this paper, we consider maximizing the geometric margin of the classifier. Intuitively, a large margin relates to classifier robustness. We introduce novel margin maximization objective for deep neural networks. We theoretically show that the proposed objective is equivalent to the robust optimization problem for a neural network. Our work seamlessly generalizes SVM margin objective to deep neural networks. In the experiments, we extensively verify the effectiveness of the proposed margin maximization objective to improve neural network robustness and to reduce overfitting on MNIST and CIFAR-10 dataset.