  In the real time formalism of the finite-temperature field theory, we compute
the one-loop gluon self-energy in a semi-quark-gluon plasma (QGP) where a
background filed ${\cal Q}$ has been introduced for the vector potential,
leading to a non-trivial expectation value for the Polyakov loop in the
deconfined phase. Explicit results of the gluon self-energies up to the
next-to-leading order in the hard-thermal-loop approximation are obtained. We
find that for the retarded/advanced gluon self-energy, the corresponding
contributions at next-to-leading order are formally analogous to the well-known
result at ${\cal Q}=0$ where the background field modification on the Debye
mass is entirely encoded in the second Bernoulli polynomials. The same feature
is shared by the leading order contributions in the symmetric gluon self-energy
where the background field modification becomes more complicated, including
both trigonometric functions and the Bernoulli polynomials. These contributions
are non-vanishing and reproduce the correct limit as ${\cal Q} \rightarrow 0$.
In addition, the leading order contributions to the retarded/advanced gluon
self-energy and the next-to-leading order contributions to the symmetric gluon
self-energy are completely new as they only survive at ${\cal Q}\neq0$. Given
the above results, we explicitly verify that the Kubo-Martin-Schwinger
condition can be satisfied in a semi-QGP with non-zero background field.
