The existing reconstruction methods for susceptibility tensor imaging assume that frequency shifts are purely from magnetic susceptibility effects, which may result in noise and error propagation in the calculated susceptibility quantities. In this study, we proposed an extended asymmetric susceptibility tensor model that introduced the non-susceptibility-induced frequency shift, i.e. offset term. Simulation, ex vivo, and in vivo data were reconstructed using the proposed model and compared models. Experimental results show that the proposed method leads to more discernable fiber structures and more accurate fiber orientation estimation. This study inspires STI reconstruction from the perspective of better modeling frequency sources.