Low-temperature thermal conductivity(κ), as well as the magnetic properties and specific heat, are studied for the frustrated zigzag spin-chain material Sr Er2O4 by using single-crystal samples. The specific heat data indicate the longrange antiferromagnetic transition at ~0.73 K and the existence of strong magnetic fluctuations. The magnetizations at very low temperatures for magnetic field along the c axis(spin chain direction) or the a axis reveal the field-induced magnetic transitions. The κ shows a strong dependence on magnetic field, applied along the c axis or the a axis, which is closely related to the magnetic transitions. Furthermore, high magnetic field induces a strong increase of κ. These results indicate that thermal conductivity along either the c axis or the a axis are mainly contributed by phonons, while magnetic excitations play a role of scattering phonons.