  In this paper, we give a systematic theoretical study on the Landau levels
(LLs) and magneto-optical conductivity Re$(\sigma_{\alpha\alpha})$ in a gapped
Dirac semimetal model with mixed linear and parabolic dispersions under a
magnetic field, which was recently proposed by Jiang \textit{et al.} [Phys.
Rev. Lett. {\bf125}, 046403 (2020)] to explain the experimental magnetoinfrared
spectroscopy in the three-dimensional ZrTe$_5$ crystal. We find that the strong
magnetic field can drive the LLs become noninverted and thus the strong
topological insulator phase in ZrTe$_5$ turns to be a trivial insulator. In the
different magnetic field regions, the density of states and
Re$(\sigma_{\alpha\alpha})$ can exhibit distinct signatures. Moreover, when the
magnetic field is weak, a qualitative relation in Re$(\sigma_{zz})$ between the
peaks at the saddle points is revealed as
Re$(\sigma_{zz}^{\zeta_n})>$Re$(\sigma_{zz}^\Gamma)$, which is in good
agreement with the experiment.
