  We study the quasinormal mode of the perturbation of the scalar field
interacting with the electromagnetic field in the backgrounds of Schwarzschild
AdS black hole, the Reissner-Nordstrom AdS black hole and the Born-Infeld AdS
black hole. We disclose influence by the electric charge $Q$, the coupling
between the scalar and electromagnetic field $q$ and the Born-Infeld parameter
$b$ on the quasinormal frequencies of the scalar perturbation. We observe the
possible growing mode in the perturbation when the scalar field strongly
couples to the electromagnetic field. When the electromagnetic field becomes
nonlinear described by the Born-Infeld electrodynamics, the nonlinearity
described by the Born-Infeld parameter can hinder the growing mode to appear in
the scalar perturbation. The quasinormal mode of the scalar field perturbation
can help us further understand the physics in the holographic superconductor.
