Quantitative Susceptibility Mapping (QSM) is a powerful MRI technique to quantify susceptibility changes and reveal pathology such as multiple sclerosis (MS) lesions and demyelination. QSM reconstruction is very challenging because it requires solving an ill-posed deconvolution and removing the effects of a dipole kernel on tissue phases to obtain susceptibility. To address the limitations of existing QSM reconstruction methods in accuracy, stability and efficiency, an iteration-free data-driven QSM reconstruction is proposed that trains a deep learning model to approximate COSMOS QSM quantification from acquired signals and pre-processed phases. Cross-validated on in-vivo datasets with 15 single direction QSM scans and 3 COSMOS QSM results from 3 healthy subjects, the proposed deep learning method achieves accurate QSM reconstruction, outperforming state-of-the-art methods across various metrics. The deep learning solution is also faster than iterative reconstruction by several orders of magnitude, which enables broader clinical applications.