  An accurate theoretical template of the redshift-space galaxy power spectrum,
if applicable out to nonlinear scales, enables us to extract more stringent and
robust constraints on cosmological parameters from the measured galaxy
clustering. In this work, we develop a simulation-based template, so-called
emulator, for the redshift-space power spectrum of dark matter halos. Using the
redshift-space halo power spectra measured from the Dark Quest $N$-body
simulation suite that covers 101 flat-geometry $w$CDM cosmologies around the
Planck $\Lambda$CDM model, we feed these data into a feed-forward neural
network to build the fast and accurate emulation of the power spectrum from the
linear to nonlinear scales up to $k \simeq 0.6 \,h \,{\rm Mpc}^{-1}$. Our
emulator achieves about 1% and 5% fractional accuracies in predicting the
monopole and quadrupole moments of the power spectrum, respectively, for halos
of $\sim 10^{13}h^{-1}M_\odot$ that correspond to host halos of the SDSS LOWZ-
and CMASS-like galaxies, where the achieved accuracies are sufficient compared
to the statistical errors of SDSS volume. The validation and performance of the
emulator are given by the comparison of the emulator predictions with the power
spectra directly measured from the simulations for validation sets that are not
used in the training. We demonstrate that the emulator outputs can be used to
make model predictions for the redshift-space power spectrum of galaxies by
employing user-fed models for the halo-galaxy connection, such as the halo
occupation distribution. The emulator allows us to easily incorporate the
Finger-of-God effect due to the virial motions of galaxies and the
Alcock-Paczy\'{n}ski distortions. Our code can compute the redshift-space
galaxy power spectrum in a CPU subseconds and is ready to perform the
emulator-based cosmological analysis for the exiting and upcoming galaxy
redshift surveys.
