Current deep learning (DL) techniques for quantitative susceptibility mapping (QSM) reconstruction demonstrated improved performance of QSM reconstruction compared with conventional non-DL methods. However, these end-to-end supervised DL techniques usually require a large amount of labeled training pairs and can be limited to the inherent difficulties of measuring `ground-truth' in QSM. In light of these, we presented an unsupervised DL method for QSM inversion denoted as uQSM. Without accessing to QSM labels, uQSM was trained to perform QSM reconstruction using the physical model. When evaluating multi-orientation QSM datasets, uQSM results have achieved higher levels of quantitative accuracy compared to TKD, TV-FANSI, and MEDI approaches. Additionally, uQSM can better preserve susceptibility anisotropy and microstructures in comparison with QSMnet and COSMOS. In addition, uQSM was evaluated on a large number of single-orientation QSM datasets. Visual assessment showed that uQSM outperformed conventional non-DL QSM reconstruction methods.