Full-duplex systems require very strong self-interference cancellation in order to operate correctly and a significant part of the self-interference signal is due to non-linear effects created by various transceiver impairments. As such, linear cancellation alone is usually not sufficient and sophisticated non-linear cancellation algorithms have been proposed in the literature. In this work, we investigate the use of a neural network as an alternative to the traditional non-linear cancellation method that is based on polynomial basis functions. Measurement results from a full-duplex testbed demonstrate that a small and simple feed-forward neural network canceler works exceptionally well, as it can match the performance of the polynomial non-linear canceler with significantly lower computational complexity.