We propose to use Deep Neural Networks to solve data-driven stochastic optimization problems. Given the historical data of the observed covariate, taken decision, and the realized cost in past periods, we train a neural network to predict the objective value as a function of the decision and the covariate. Once trained, for a given covariate, we optimize the neural network over the decision variable using gradient-based methods with the analytically-computed gradient and Hessian matrix. We characterize the performance of our methodology based on the generalization bound of the neural network. We conduct comprehensive experiments on three signature problems in operations management: the newsvendor problem, the multi-product pricing problem, and the call center staffing problem. Comparing our framework to existing approaches including conditional stochastic optimization and analytical approximations, we demonstrate the strength of our method when the objective function is unknown, with moderate size data, and when the structure of the problem cannot be approximated by simple or parametric forms.