  A primordial black hole (PBH) is interesting to people for its ability of
explaining dark matter as well as supermassive astrophysical objects. In the
normal inflation scenario, the generation of PBHs usually requires an enhanced
power spectrum of scalar perturbation at the end of inflation era, which is
expected when the dispersion relation of the inflaton field gets modified. In
this work, we study a kind of inflation model called {the \it
Dirac-Born-Infeld-inspired nonminimal kinetic coupling (DINKIC)} model, where
the dispersion relation is modified by a square root existing in the field
Lagrangian. We discuss the enhancement of scalar power spectrum due to the
modified dispersion relation, as well as the abundance of PBHs produced by the
Press-Schechter collapse mechanism. We also discuss the formation of
scalar-induced gravitational waves by linear scalar perturbations.
