  We investigate the quasinormal modes of a class of static and spherically
symmetric black holes with the derivative coupling. The derivative coupling has
rarely been paid attention to the study of black hole quasinormal modes.
Specifically, we study the effect of derivative coupling on the quasinormal
modes for four kinds of black holes. They are Reissner-Nordstrom black holes,
Bardeen black holes, noncommunicative geometry inspired black holes and dilaton
black holes. These black holes are not the solutions of vacuum Einstein
equations which guarantees the effect of derivative coupling is not trivial. We
find the influence of derivative coupling on the quasinormal modes roughly
mimics the overtone numbers. In other words, there is a qualitative similarity
in the trend of quasinormal modes frequencies due to increasing either the
coupling constant and the overtone number.
