A method is proposed that applies an artificial neural network model to estimate an origin-destination (O-D) matrix for a freeway network for which the data on inflow and outflow at the ramps are gathered regularly. This problem is the same as estimating the elements of an O-D table, given that many sets of data about the right-hand column total (trip production) and the bottom row total (trip attraction) are available. A neural network model is developed to emulate the stimulus-response process on the freeway traffic, in which the stimulus is the inflow at the entrance ramps and the response the outflow at the exit ramps. After the neural network of a particular structure is trained by many sets of data (e.g., sets of daily volumes), the weights of the neural network are found to represent the ramp-to-ramp volume expressed in the proportion of the inflow at the corresponding ramps. The model is applied to estimate a ramp-to-ramp O-D table for the Tokyo expressway network. The result is compared with the actual O-D table obtained from a survey. The model is found to be useful not only for estimating the O-D volume with much less data than for the traditional method, but also for verifying the existence of a pattern in the traffic flow.