For flight dynamics modeling of a missile system to predict trajectories, very efficient aerodynamic models with at least conceptual design level fidelity are required because of the extreme diversity in flight conditions encountered. This paper presents a Deep Learning Neural Network (DNN) based approach for predicting 5 missile aerodynamic coefficients (dependent variables). This approach has been implemented for a diversity of grid fin equipped missile configurations. For this paper, no canards are incorporated in the training data sets. For this demonstration effort, a lower order physics model for the aerodynamics has been used to generate training and validation data. A single center body geometry has been considered in this analysis with a full range of grid fin semi spans, cell sizes, Mach numbers, incident angles, and angles of attack have been considered (a total of 8 predictor variables). In this investigation, techniques were developed for selecting an appropriately small subset of the data for training DNNs and using the larger remainder of the data for testing. Results presented in this work point the way toward modeling aerodynamics of grid fin equipped missile systems with high fidelity using a very limited set of high resolutions computational fluid dynamics solutions.