Signatures of van Hove singularities in the anisotropic in-plane optical conductivity of the topological semimetal <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi mathvariant="normal">Nb</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">SiTe</mml:mi><mml:mn>6</mml:mn></mml:msub></mml:math>

We present a temperature-dependent infrared spectroscopy study on the layered topological semimetal Nb$_3$SiTe$_6$ combined with density-functional theory (DFT) calculations of electronic band structure and optical conductivity. Our results reveal an anisotropic behavior in-plane ($ac$-plane) conductivity, three pronounced excitations located at around 0.15, 0.28, 0.41~eV for polarization incident radiation along $c$ axis. These are well reproduced in theoretical spectra. Based \textit{ab initio} results, 0.15 eV 0.28 interpreted as fingerprints van Hove singularities compared to findings other semimetals.