Recently layered compound $\mathrm{TaNi}{\mathrm{Te}}_{5}$ was proposed to be two-dimensional (2D) topological semimetals. Here we report the detailed investigation on $\mathrm{TaNi}{\mathrm{Te}}_{5}$ single crystals through magnetotransport and de Hass\ensuremath{-}van Alphen (dHvA) effect studies. Strong quantum oscillations with multiple periodicities have been observed. By analyzing the quantum oscillations, we provide evidence of nontrivial Berry phase with a 3D Fermi surface character in layered $\mathrm{TaNi}{\mathrm{Te}}_{5}$. Our work suggested that layered $\mathrm{TaNi}{\mathrm{Te}}_{5}$ should be 3D topological semimetal which offers a platform to explore exotic properties in low-dimensional topological semimetals.