  The scientific aim of the space gravitational wave (GW) detector Laser
Interferometer Space Antenna (LISA) that was scheduled to launch in the early
2030s is to detect the low-frequency GW signals in the Galaxy. Its main
candidate GW sources are compact binaries of white dwarfs and neutron stars. In
this work, we examine whether compact intermediate-mass black hole (IMBH) X-ray
binaries could be potential LISA sources. Our simulations indicate that IMBH
binary with a 1000 $M_{\odot}$ IMBH and a 3 $M_{\odot}$ donor star in an orbit
of initial orbital period near the so-called bifurcation period of 0.77 d could
evolve into an ultra-compact X-ray binary, which will emit GW signals with
maximum frequency of 2.5 mHz. According to the evolutionary tracks of
characteristic strain, IMBH X-ray binaries with the initial donor-star masses
of $1-3~M_{\odot}$ and the initial orbital periods slightly less than the
bifurcation periods will be detectable by the LISA in a distance of 15 kpc.
Assuming each of 60 Galactic globular clusters hosts a 1000 $M_{\odot}$ IMBH,
the maximum number of compact IMBH X-ray binaries that LISA will detect in the
Galaxy should be less than ten. Therefore, the detectability of compact IMBH
X-ray binaries by the LISA is not optimistic.
