  By proposing a pure leptonic radiation model, we study the potential
gamma-ray emissions from jets of the low-mass X-ray binaries. In this model,
the relativistic electrons that are accelerated in the jets are responsible for
radiative outputs. Nevertheless, dynamics of jets are dominated by the magnetic
and proton-matter kinetic energies. The model involves all kinds of related
radiative processes and considers the evolution of relativistic electrons along
the jet by numerically solving the kinetic equation. Numerical results show
that the spectral energy distributions can extend up to TeV bands, in which
synchrotron radiation and synchrotron self-Compton scattering are dominant
components. As an example, we apply the model to the low-mass X-ray binary GX
339-4. The results can not only reproduce the currently available observations
from GX 339-4, but also predict detectable radiation at GeV and TeV bands by
Fermi and CTA telescopes. The future observations with Fermi and CTA can be
used to test our model, which could be employed to distinguish the origin of
X-ray emissions.
