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The fascinating liquid-like behavior of the Fe3O4/polyaniline (Fe3O4/PANI) solvent-free nanofluid permits some important applications of which. However, for the lack of the investigation on the magnetic response mechanism of the Fe3O4/PANI solvent-free nanofluid, the precise magnetic control on the liquid-like behaviors of the Fe3O4/PANI solvent-free nanofluid is difficult. Thus, the magnetic field response of the Fe3O4/PANI solvent-free nanofluid is investigated employing a complex structure-preserving approach in this paper. Considering one branch chain grafting on the Fe3O4/PANI nanoparticle, a flexible hub-beam model is proposed. The dynamic equations of the flexible magnetic hub-beam model subjected to the external magnetic field force and the viscous resistance are deduced in the Lagrangian framework. Combing the symplectic precise integration method and the generalized multi-symplectic method, a complex structure-preserving approach is developed to study the magnetic field response characteristics of the Fe3O4/PANI solvent-free nanofluid. From the numerical results, the upper limit of the stable moving speed of the Fe3O4/PANI solvent-free nanofluid is obtained. In addition, the effects of the model parameters (including the external magnetic field strength as well as the length of the branch chain) on the upper limit of the stable moving speed of the Fe3O4/PANI solvent-free nanofluid are analyzed. The above results can be used to guide the magnetic control strategy design for the rheological property of the magnetic solvent-free nanofluid.