We observed the brightest part of HESS J1825-137 with the Suzaku XIS, and found diffuse X-rays extending at least up to 15 (~ 17 pc) from the pulsar PSR J1826-1334. The spectra have no emission line, and are fitted with an absorbed power-law model. T
he X-rays, therefore, are likely due to synchrotron emission from a pulsar wind nebula. The photon index near at the pulsar (r<1.5) is 1.7 while those in r=1.5-16 are nearly constant at Gamma=2.0. The spectral energy distribution of the Suzaku and H.E.S.S. results are naturally explained by a combined process; synchrotron X-rays and gamma-rays by the inverse Compton of the cosmic microwave photons by high-energy electrons in a magnetic field of 7 micro G. If the electrons are accelerated at the pulsar, the electrons must be transported over 17 pc in the synchrotron life time of 1900 yr, with a velocity of > 8.8 times 10^3 km s^{-1}.
