ABSTRACT Ultrafast 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 ($10^{9}\!-\!4.5\times 10^{12}\, \mathrm{cm}^{-3}$) 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 ($L_\mathrm{UFO}\sim 4.4~{{\ \rm per\ cent}}\, L_\mathrm{Edd}$), reaching the theoretical criterion to affect the evolution of the host galaxy. We also find that emission lines, from a large-scale region, have a blueshift of 2700–4500 km s−1 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.