To perform close proximity operations under a low-gravity environment, relative and absolute positions are vital information to the maneuver. Hence navigation is inseparably integrated in space travel. Extreme Learning Machine (ELM) is presented as an optical navigation method around small celestial bodies. Optical Navigation uses visual observation instruments such as a camera to acquire useful data and determine spacecraft position. The required input data for operation is merely a single image strip and a nadir image. ELM is a machine learning Single Layer feed-Forward Network (SLFN), a type of neural network (NN). The algorithm is developed on the predicate that input weights and biases can be randomly assigned and does not require back-propagation. The learned model is the output layer weights which are used to calculate a prediction. Together, Extreme Learning Machine Optical Navigation (ELM OpNav) utilizes optical images and ELM algorithm to train the machine to navigate around a target body. In this thesis the asteroid, Vesta, is the designated celestial body. The trained ELMs estimate the position of the spacecraft during operation with a single data set. The results show the approach is promising and potentially suitable for on-board navigation.