  We investigate the holographic entanglement entropy in the
insulator/superconductor phase transition for the Born-Infeld electrodynamics
with full backreaction in five-dimensional AdS soliton spacetime. We note that
the holographic entanglement entropy is a good probe to study the properties of
the phase transition, and the Born-Infeld factor $b$ has no effect on the
critical chemical potential $\mu_c$. We find that both in the half space and
the belt one, the non-monotonic behavior of the entanglement entropy versus the
chemical potential is a general property, and the entanglement entropy
increases with the increase of the Born-Infeld factor in the superconductor
phase. Particularly, there exists confinement/deconfinement phase transition in
the strip geometry and the critical width $\ell_c$ is dependent of the
Born-Infeld parameter.
