In this work, the linearity property of a recently proposed neural network-based QSM is explored. The QSMnet, which was trained using healthy volunteers, was quantitatively evaluated for patients with hemorrhage whose susceptibility values were outside of the trained range. The results showed that the QSMnet underestimated the susceptibility in hemorrhage, breaking linearity between true susceptibility and QSMnet-generated susceptibility. To overcome this limitation, we developed a linear scaling method that generalized the network for a wider range of susceptibility. The new network successfully reconstructed the patient data with good linearity results.