  Three dimensional (3D) topological Dirac materials are under intensive study
recently. The layered compound ZrTe$_5$ has been suggested to be one of them by
transport and ARPES experiments. Here, we perform infrared reflectivity
measurement to investigate the underlying physics of this material. The derived
optical conductivity exhibits linear increasing with frequency below normal
interband transitions, which provides the first optical spectroscopic proof of
a 3D Dirac semimetal. Apart from that, the plasma edge shifts dramatically to
lower energy upon temperature cooling, which might be associated with the
consequence of lattice parameter shrinking. In addition, an extremely sharp
peak shows up in the frequency dependent optical conductivity, indicating the
presence of a Van Hove singularity in the joint density of state.
