The spin Hall magnetoresistance (SMR) effect in Pt/Gd₃Fe₅O₁₂ (GdIG) bilayers was systematically investigated. The sign of SMR changes twice with increasing magnetic field in the vicinity of the magnetization compensation point (T _M) of GdIG. However, conventional SMR theory predicts the invariant SMR sign in the heterostructure composed of a heavy metal film in contact with a ferromagnetic or antiferromagnetic film. We conclude that this is because of the significant enhancement of the magnetic moment of the Gd sub-lattice and the unchanged moment of the Fe sub-lattice with a relatively large field, meaning that a small net magnetic moment is induced at T _M. As a result, the Nel vector aligns with the field after the spin-flop transition, meaning that a bi-reorientation of the Nel vector is produced. Theoretical calculations based on the Nel’s theory and SMR theory also support our conclusions. Our findings indicate that the Nel-vector direction of a ferrimagnet can be tuned across a wide range by a relatively low external field around T _M.