The localization of structural defects is of great interest in structure health monitoring (SHM). While acoustic emission signals are collected in the practice of SHM, the acquired waveforms inevitably include direct wave as well as reflection and reverberation waveforms. The direct wave actually contains more straightforward information in localizing the sources, so in this work, a deep recurrent denoising autoencoder (DRDA) network is developed. In general, waveform signals are highly correlated at different timescales, so temporally recurrent connections are added to the network structure, which have the memory of recent inputs. Consequently, the proposed DRDA model captures the dependencies across data points, while carrying out denoisng process, and combines the advantages of denoising autoencoders and recurrent neural networks. As the output of the proposed DRDA, direct waveforms are extracted and validated through finite element simulations. A contrived structure with nontrivial shape is excited by simulated pencil break excitations under the ABAQUS environment, then the simulated responses provide training data for the DRDA. The proposed algorithm is effective in filtering the reflected wave and outperforms the conventional denoising autoencoders.