  PSR 1259-63 is a radio pulsar orbiting a Be star in a highly eccentric orbit.
Soft and hard X-rays are observed from this binary system. We apply the shock
powered emission model to this system. The collision of the pulsar and Be star
winds forms a shock, which accelerates electrons and positrons to the
relativistic energies. We derive the energy distribution of relativistic
electrons and positrons as a function of the distance from the shock in the
pulsar nebula. We calculate the X-rays and $\gamma$-rays emitted from the
relativistic electrons and positrons in the nebula at various orbital phases,
taking into account the Klein-Nishina effect fully. The shock powered emission
model can explain the observed X-ray properties approximately. We obtain from
the comparison with observations that a fraction of $\sim 0.1$ of the pulsar
spin-down luminosity should be transformed into the relativistic electrons and
positrons. We find that the magnetization parameter of the pulsar wind, the
ratio of the Poynting flux to the kinetic energy flux, is $\sim 0.1$
immediately upstream of the termination shock of the pulsar wind, and may
decrease with distance from the pulsar. We predict the flux of 10 MeV - 100 GeV
$\gamma$-rays which may be nearly equal to the detection threshold in the
future projects.
