We report spectral and timing analysis of the black hole transient MAXI J1631–479 during the hard intermediate state of its 2019 outburst from the Insight-Hard X-ray Modulation Telescope (Insight-HXMT) observations. We find that the energy dependence of the type-C quasi-periodic oscillation (QPO) frequency evolves with time: during the initial rise of a small flare (∼MJD 58526.0-58527.1), the QPO frequency increases with increasing energy from ∼1 to ∼100 keV, and then the frequency remains constant after MJD 58527.1. We discover a possible new phenomenon of Fe line’s QPO frequency jump that has never been observed for other black hole transients: during the small flare, the QPO frequency around the Fe line energy is higher than any other energy band, with the frequency difference Δf = 0.25 ± 0.08 Hz between 5.5–7.5 keV and other energy bands. The spectral analysis shows that the evolution of QPOs is related to the equivalent width of the narrow Fe line, and its equivalent width increases during this small flare. We propose that the QPO frequency difference results from the differential precession of a vertically extended jet, and the higher QPO frequency of Fe line could be caused by the layered jet when the jet scale increases. At the same time, the evolution of QPOs is related to the accretion rate, while the energy dependence of QPOs supports the existence of deceleration in the vertically distributed jet.