  The transverse momentum spectrum of $\eta$ meson in relativistic heavy-ion
collisions is studied at the next-to-leading-order (NLO) within the
perturbative QCD, where the jet quenching effect in the QGP is incorporated
with the effectively medium-modified $\eta$ fragmentation functions using the
higher-twist approach. We show that the theoretical simulations could give nice
descriptions of PHENIX data on $\eta$ meson in both $\rm p+p$ and central $\rm
Au+Au$ collisions at the RHIC, and also provide numerical predictions of $\eta$
spectra in central $\rm Pb+Pb$ collisions with $\sqrt{s_{NN}}=2.76$~TeV at the
LHC. The ratios of $\eta/\pi^0$ in $\rm p+p$ and in central $\rm Au+Au$
collisions at $200$~GeV are found to overlap in a wide $p_T$ region, which
matches well the measured ratio $\eta / \pi^0$ by PHENIX. We demonstrate that,
at the asymptotic region when $p_{T} \rightarrow \infty$ the ratios of
$\eta/\pi^{0}$ in both $\rm Au+Au$ and $\rm p+p$ are almost determined only by
quark jets fragmentation and thus approach to the one in $e^{+} e^{-}$
scattering; in addition, the almost identical gluon (quark) contribution
fractions to $\eta$ and to $\pi$ result in a rather moderate variation of
$\eta/\pi^{0}$ distribution at intermediate and high $p_T$ region in $\rm A+A$
relative to that in $\rm p+p$; while a slightly higher $\eta/\pi^{0}$ at small
$p_T$ in $\rm Au+Au$ can be observed due to larger suppression of gluon
contribution fraction to $\pi^{0}$ as compared to the one to $\eta$. The
theoretical prediction for $\eta / \pi^0$ at the LHC has also been presented.
