  The dark matter halo has non-negligible effects on the gravitational lensing
of supermassive black hole in the galaxy center. Our work presents a study on
the time-delay of light in gravitational lensing of black holes enclosed by
dark matter halos. To provide a precise description on the distribution of dark
matter in galaxies, we choose several famous phenomenological dark matter halo
models in astrophysics, including the NFW, Beta, Burkert and Moore models, to
carry out the present study. Through numerically calculating the time-delay of
light in gravitational lensing, a comparative analysis of the dark matter
effects within different halo models has been performed. Assuming typical
length scales associated with the galactic gravitational lensing, numerical
results indicate that the NFW, Beta, Burkert and Moore dark matter halos can
significantly enhance the time delay of light in gravitational lenisng of
central supermassive black holes. The enhancing effect becomes more pronounced
with a small dark matter halo scale and an increasing dark matter halo mass.
  Keywords: Black Hole; Gravitational Lensing; Time Delay; Dark Matter Halo
