Close proximity operations around small bodies are extremely challenging due to their uncertain dynamical environment. Autonomous guidance and navigation around small bodies require fast and accurate modeling of the gravitational field for potential on-board computation. In this paper, we investigate a model-based, data-driven approach to compute and predict the gravitational acceleration around irregular small bodies. More specifically, we employ Extreme Learning Machine (ELM) theories to design, train and validate Single-Layer Forward Networks (SLFN) capable of learning the relationship between the spacecraft position and the gravitational acceleration. ELMs-base neural networks are trained without iterative tuning therefore dramatically reducing the training time. Analysis of performance in constant density models for 433 Eros and 25143 Itokawa show that ELM-based SLFN are able learn the desired functional relationship both globally and in localized areas near the surface. The latter results in a robust neural algorithm for on-board, real-time calculation of the gravity field needed for close-proximity operations near the asteroid surface.