  A model of nonlinear electrodynamics with two parameters, coupled with
general relativity, is investigated. We study the magnetized black hole and
obtain solutions. The asymptotic of the metric and mass functions at
$r\rightarrow\infty$ and $r\rightarrow 0$, and corrections to the
Reissner-Nordstr\"{o}m solution are found. We investigate thermodynamics of
black holes and calculate the Hawking temperature and heat capacity of black
holes. It is shown that there are phase transitions and at some parameters of
the model black holes are stable.
