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We observed the brightest part of HESS J1825-137 with the Suzaku XIS, andfound diffuse X-rays extending at least up to 15' (~ 17 pc) from the pulsar PSRJ1826-1334. The spectra have no emission line, and are fitted with an absorbedpower-law model. The X-rays, therefore, are likely due to synchrotron emissionfrom a pulsar wind nebula. The photon index near at the pulsar (r<1.5') is 1.7while those in r=1.5-16 are nearly constant at Gamma=2.0. The spectral energydistribution of the Suzaku and H.E.S.S. results are naturally explained by acombined process; synchrotron X-rays and gamma-rays by the inverse Compton ofthe cosmic microwave photons by high-energy electrons in a magnetic field of 7micro G. If the electrons are accelerated at the pulsar, the electrons must betransported over 17 pc in the synchrotron life time of 1900 yr, with a velocityof > 8.8 times 10^3 km s^{-1}.

Suzaku Observation of HESS J1825-137: Discovery of Largely-Extended X-rays near from PSR J1826-1334