In the Galaxy, close binaries with compact objects are important low-frequency gravitational wave (GW) sources. As potential low-frequency GW sources, neutron star/white dwarf (WD) ultracompact X-ray binaries (UCXBs) have been investigated extensively. Using the Modules for Experiments in Stellar Astrophysics code, we systematically explored the evolution of black hole (BH)-main-sequence star (MS) binaries to determine whether their descendants can be detected by space-borne GW detectors. Our simulations showed that BH-MS binaries with an initial orbital period less than the bifurcation period can evolve into BH UCXBs that can be detected by LISA. Such an evolutionary channel would form compact mass-transferring BH-WD systems rather than detached BH-WD systems. The calculated X-ray luminosities of BH UCXBs that can be detected by LISA at a distance d = 1 kpc are ∼1033–1035 erg s−1 (∼1034–1035 erg s−1 for d = 10 kpc); hence, it is possible to detect their electromagnetic counterparts. It is worth emphasizing that only some BH-MS systems with an initial orbital period very close to the bifurcation period can evolve toward low-frequency GW sources whose chirp masses can be measured. The maximum GW frequency of BH UCXBs forming via the BH-MS pathway is about 3 mHz, which is smaller than the minimum GW frequency (6.4 mHz) of mass-transferring BH-WDs originating from a dynamic process. Furthermore, we obtain an initial parameter space (donor-star masses and orbital periods) of progenitors of BH UCXB-GW sources, which can be applied to future population synthesis simulations. By a rough estimation, we predict that LISA would only be able to detect a few BH UCXB-GW sources formed by the BH-MS channel.