HESS J1825–137 was detected with a significance of 8.1 σ in the Galactic Plane survey conducted with the H.E.S.S. instrument in 2004. Both HESS J1825–137 and the X-ray pulsar wind nebula G18.0–0.7 (associated with the Vela-like pulsar PSR B1823–13) are offset south of the pulsar, which may be the result of the SNR expanding into an inhomogeneous medium. The TeV size (∼ 35 pc, for a distance of 4 kpc) is ∼ 6 times larger than the X-ray size, which may be the result of propagation effects as a result of the longer lifetime of TeV emitting electrons, compared to the relatively short lifetime of keV synchrotron emitting electrons. The TeV photon spectral index of ∼ 2.4 can also be related to the extended PWN X-ray synchrotron photon index of ∼ 2.3, if this spectrum is dominated by synchrotron cooling. The anomalously large size of the pulsar wind nebula can be explained if the pulsar was born with a relatively large initial spindown power and braking index n ∼ 2, provided that the SNR expanded into the hot ISM with relatively low density (∼ 0.003 cm).