  It was shown that the dark matter(DM) minihalo around an intermediate mass
black hole(IMBH) can be redistributed into a cusp, called the DM minispike. We
consider an intermediate-mass-ratio inspiral consisting of an IMBH harbored in
a DM minispike with nonannihilating DM particles and a small black hole(BH)
orbiting around it. We investigate gravitational waves(GWs) produced by this
system and analyze the waveforms with the comprehensive consideration of
gravitational pull, dynamical friction and accretion of the minispike and
calculate the time difference and phase difference caused by it. We find that
for a certain range of frequency, the inspiralling time of the system is
dramatically reduced for smaller central IMBH and large density of DM. For the
central IMBH with $10^5M_\odot$, the time of merger is ahead, which can be
distinguished by LISA, Taiji and Tianqin. We focus on the effect of accretion
and compare it with that of gravitational pull and friction. We find that the
accretion mass is a small quantity compared to the initial mass of the small BH
and the accretion effect is inconspicuous compared with friction. However, the
accumulated phase shift caused by accretion is large enough to be detected by
LISA, Taiji and Tianqin, which indicate that the accretion effect can not be
ignored in the detection of GWs.
