  By employing the perturbative QCD (pQCD) factorization approach, we
calculated some important next-to-leading-order(NLO) contributions to the
two-body charmless hadronic decays $B^+ \to \rho^+ \eta^{(\prime)}$ and $B^0
\to \rho^0(\omega, \phi) \eta^{(\prime)}$, induced by the vertex QCD
corrections, the quark-loops as well as the chromo-magnetic penguins. From the
numerical results and phenomenological analysis we find that (a) for $B^\pm \to
\rho^\pm \etap$ decays, the partial NLO contributions to branching ratios are
small in magnitude; (b) for $B^0 \to \rho^0(\omega,\phi) \etap$ decays, the NLO
contributions can provide significant enhancements to the leading order
predictions of their branching ratios; and (c) the pQCD predictions for the
CP-violating asymmetries $\acp^{dir}(B^\pm \to \rho^\pm \etap)$ are consistent
with the data, while the predicted $\acp(B^0 \to \rho^0(\omega)\etap)$ are
generally large in magnitude and could be tested by the forthcoming LHCb
experiments.
