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Topological pentatellurides, ZrTe₅/HfTe₅, show intriguing quantum transport properties. One of the unique characteristics is the extremely small Fermi surface consisting of massive Dirac fermions. This allows the system to reach the quantum limit at a small magnetic field. Under the magnetic fields far above the quantum limit, all electrons are spin polarized and pushed into the zeroth Landau level. The increasing Zeeman energy and cyclotron energy under the magnetic field may lead to band inversion as the zeroth Landau bands cross with each other, as seen in a recent magneto-infrared spectroscopy study. Depending on the topological ground state of the system, i.e., weak topological insulator or strong topological insulator, it may result in 1D Weyl nodes in the ultra-quantum limit. We have investigated the quantum transport properties of HfTe5 under pulsed magnetic fields and found signatures of enhanced conductivity and sign changes of Hall resistivity, pointing to a Liftshitz transition, under perpendicular magnetic fields. With the magnetic field parallel to the current, the longitudinal magnetoresistance shows interesting evolutions as functions of temperature and magnetic field, which might be understood by the Zeeman splitting of the bands. Our quantum transport results shed light on how the electronic property evolves in the ultra-quantum limit in HfTe₅.