Quantitative susceptibility mapping (QSM) inevitably suffers from streaking artifacts which is caused from the zeros on the conical surface of the dipole inversion kernel. Various methods have been proposed to resolve this issue, but most of them either have difficulty in accurate mapping due to magnitude-based reconstruction, show severe streaking artifacts, or require imaging with subject positioning at various angles. In this thesis, a novel k-space interpolation based dipole inversion algorithm is proposed in order to overcome this ill-posed problem. The redundancy in the spatial domain produces the low-rank Hankel structured matrix in the Fourier domain. This implies that an artifact-free k-space data can be recovered from incomplete or distorted k-space data by constructing Hankel structured matrix and exploiting its low-rankness. Accordingly, it means the Hankel-matrix approach can be used to solve QSM inversion problem. In this paper, the numerical phantom and in-vivo brain MRI data were used for validation of the Hankel-matrix approach and comparison with other conventional methods. The proposed method effectively reduced streaking artifacts compared to the conventional methods, and the results accurately estimated magnetic susceptibility compared to reference data (COSMOS) acquired with subject positions at multiple angles. To sum up, the proposed algorithm can reconstruct the three-dimensional QSM dipole inversion problem successfully, without requiring any additional anatomical information or priory assumption. The thesis suggested a new novel approach to solve the dipole inversion problem for QSM.