  Ultra-fast outflows (UFOs) have been revealed in a large number of active
galactic nuclei (AGN) and are regarded as promising candidates for AGN feedback
on the host galaxy. The nature and launching mechanism of UFOs are not yet
fully understood. Here we perform a time- and flux-resolved X-ray spectroscopy
on four XMM-Newton observations of a highly accreting narrow-line Seyfert 1
(NLS1) galaxy, Mrk 1044, to study the dependence of the outflow properties on
the source luminosity. We find that the UFO in Mrk 1044 responds to the source
variability quickly and its velocity increases with the X-ray flux, suggesting
a high-density ($10^{9}-4.5\times10^{12}\,\mathrm{cm}^{-3}$) and radiatively
driven outflow, launched from the region within a distance of $98-6600\,
R_\mathrm{g}$ from the black hole. The kinetic energy of the UFO is
conservatively estimated ($L_\mathrm{UFO}\sim4.4\%L_\mathrm{Edd}$), reaching
the theoretical criterion to affect the evolution of the host galaxy. We also
find emission lines, from a large-scale region, have a blueshift of $2700-4500$
km/s in the spectra of Mrk 1044, which is rarely observed in AGN. By comparing
with other sources, we propose a correlation between the blueshift of emission
lines and the source accretion rate, which can be verified by a future sample
study.
