  Both the anomalous magnetic braking of Ap/Bp stars and the surrounding
circumbinary disk models can account for the formation of black hole (BH)
low-mass X-ray binaries (LMXBs), while the simulated effective temperatures of
the donor stars are significantly higher than the observed values. Therefore,
the formation of BH LMXBs is not still completely understood. In this work, we
diagnose whether the dynamical friction between dark matter and the companion
stars can drive BH binaries to evolve toward the observed BH LMXBs and
alleviate the effective temperature problem. Assuming that there exists a
density spike of dark matter around BH, the dynamical friction can produce an
efficient angular momentum loss, driving BH binaries with an intermediate-mass
companion star to evolve into BH LMXBs for a spike index higher than $\gamma =
1.58$. Our detailed stellar evolution models show that the calculated effective
temperatures can match the observed value of most BH LMXBs for a spike index
range of $\gamma = 1.7-2.1$. However, the simulated mass-transfer rates when
$\gamma = 2.0$ and $2.1$ are too high to be consistent with the observed
properties that BH LMXBs appears as soft X-ray transients. Therefore, the
dynamical friction of dark matter can only alleviate the effective temperature
problem of those BH LMXBs with a relatively short orbital period.
