Deep neural networks have demonstrated promising potential for the field of medical image reconstruction, successfully generating high quality images for CT, PET and MRI. In this work, an MRI reconstruction algorithm, which is referred to as quantitative susceptibility mapping (QSM), has been developed using a deep neural network in order to perform dipole deconvolution, which restores magnetic susceptibility source from an MRI field map. Previous approaches of QSM require multiple orientation data (e.g. Calculation of Susceptibility through Multiple Orientation Sampling or COSMOS) or regularization terms (e.g. Truncated K-space Division or TKD; Morphology Enabled Dipole Inversion or MEDI) to solve an ill-conditioned dipole deconvolution problem. Unfortunately, they either entail challenges in data acquisition (i.e. long scan time and multiple head orientations) or suffer from image artifacts. To overcome these shortcomings, a deep neural network, which is referred to as QSMnet, is constructed to generate a high quality susceptibility source map from single orientation data. The network has a modified U-net structure and is trained using COSMOS QSM maps, which are considered as gold standard. Five head orientation datasets from five subjects were employed for patch-wise network training after doubling the training data using a model-based data augmentation. Seven additional datasets of five head orientation images (i.e. total 35 images) were used for validation (one dataset) and test (six datasets). The QSMnet maps of the test dataset were compared with the maps from TKD and MEDI for their image quality and consistency with respect to multiple head orientations. Quantitative and qualitative image quality comparisons demonstrate that the QSMnet results have superior image quality to those of TKD or MEDI results and have comparable image quality to those of COSMOS. Additionally, QSMnet maps reveal substantially better consistency across the multiple head orientation data than those from TKD or MEDI. As a preliminary application, the network was further tested for three patients, one with microbleed, another with multiple sclerosis lesions, and the third with hemorrhage. The QSMnet maps showed similar lesion contrasts with those from MEDI, demonstrating potential for future applications.