Topological semimetal may have substantial applications in electronics, spintronics and quantum computation. Recently, ZrTe is predicted as a new type of topological semimetal due to coexistence of Weyl fermion and massless triply degenerate nodal points. In this work, the elastic and transport properties of ZrTe are investigated by combining the first-principles calculations and semiclassical Boltzmann transport theory. Calculated elastic constants prove mechanical stability of ZrTe, and the bulk modulus, shear modulus, Youngs modulus and Possions ratio also are calculated. It is found that spin-orbit coupling (SOC) has slightly enhanced effects on Seebeck coefficient, which along a(b) and c directions for pristine ZrTe at 300 K is 46.26 $mu$V/K and 80.20 $mu$V/K, respectively. By comparing the experimental electrical conductivity of ZrTe (300 K) with calculated value, the scattering time is determined for 1.59 $times$ $10^{-14}$ s. The predicted room-temperature electronic thermal conductivity along a(b) and c directions is 2.37 $mathrm{W m^{-1} K^{-1}}$ and 2.90 $mathrm{W m^{-1} K^{-1}}$, respectively. The room-temperature lattice thermal conductivity is predicted as 17.56 $mathrm{W m^{-1} K^{-1}}$ and 43.08 $mathrm{W m^{-1} K^{-1}}$ along a(b) and c directions, showing very strong anisotropy. Calculated results show that isotope scattering produces observable effect on lattice thermal conductivity. It is noted that average room-temperature lattice thermal conductivity of ZrTe is slightly higher than that of isostructural MoP, which is due to larger phonon lifetimes and smaller Gr$mathrm{ddot{u}}$neisen parameters. Finally, the total thermal conductivity as a function of temperature is predicted for pristine ZrTe.
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