We present an articulatory-based method for real-time accent conversion using deep neural networks (DNN). The approach consists of two steps. First, we train a DNN articulatory synthesizer for the non-native speaker that estimates acoustics from contextualized articulatory gestures. Then we drive the DNN with articulatory gestures from a reference native speaker — mapped to the nonnative articulatory space via a Procrustes transform. We evaluate the accent-conversion performance of the DNN through a series of listening tests of intelligibility, voice identity and nonnative accentedness. Compared to a baseline method based on Gaussian mixture models, the DNN accent conversions were found to be 31% more intelligible, and were perceived more native-like in 68% of the cases. The DNN also succeeded in preserving the voice identity of the nonnative speaker.