We present a magneto-infrared spectroscopy study on a newly identified three-dimensional (3D) Dirac semimetal ZrTe$_5$. We observe clear transitions between Landau levels and their further splitting under magnetic field. Both the sequence of transiti
ons and their field dependence follow quantitatively the relation expected for 3D emph{massless} Dirac fermions. The measurement also reveals an exceptionally low magnetic field needed to drive the compound into its quantum limit, demonstrating that ZrTe$_5$ is an extremely clean system and ideal platform for studying 3D Dirac fermions. The splitting of the Landau levels provides a direct and bulk spectroscopic evidence that a relatively weak magnetic field can produce a sizeable Zeeman effect on the 3D Dirac fermions, which lifts the spin degeneracy of Landau levels. Our analysis indicates that the compound evolves from a Dirac semimetal into a topological line-node semimetal under current magnetic field configuration.
