Protein structure prediction is an important problem in computational biology, and is widely applied to various biomedical problems such as protein function study, protein design, and drug design. In this work, we developed a novel deep learning approach based on a deeply stacked denoising autoencoder for protein structure reconstruction. We applied our approach to a template-based protein structure prediction using only the 3D structural coordinates of homologous template proteins as input. The templates were identified for a target protein by a PSI-BLAST search. 3DRobot (a program that automatically generates diverse and well-packed protein structure decoys) was used to generate initial decoy models for the target from the templates. A stacked denoising autoencoder was trained on the decoys to obtain a deep learning model for the target protein. The trained deep model was then used to reconstruct the final structural model for the target sequence. With target proteins that have highly similar template proteins as benchmarks, the GDT-TS score of the predicted structures is greater than 0.7, suggesting that the deep autoencoder is a promising method for protein structure reconstruction.