  Recently, we obtained the simple metrics of a spherically symmetric black
hole in a dark matter halo, and extended to the case of rotation. As the
characteristic sound of black holes, quasinormal modes (QNMs) are one of the
important means to understand black holes currently. Based on these two metrics
of a spherically symmetric black hole, we study the QNMs of cold dark matter
(CDM) and scalar field dark matter (SFDM) models using the methods of the
material field perturbations and the gravitational perturbation, and make
comparisons with the Schwarzschild black hole. Our results show that black hole
QNMs of CDM and SFDM in a dark matter halo are different from the Schwarzschild
black hole, unlike a Schwarzschild black hole with a prominent power-law tail.
The different kinds models of dark matter can be distinguished by their QNMs.
The time of QNMs ringing and frequencies increase with increasing parameter
$l$. The overall QNMs of CDM are stronger than that of SFDM in the same
condition, which is easier to be detected. In addition, QNMs frequencies using
the sixth-order WKB method and the Prony method are in good agreement.
