  A new model of nonlinear electrodynamics with two parameters is proposed. We
study the phenomenon of vacuum birefringence, the causality and unitarity in
this model. There is no singularity of the electric field in the center of
point-like charges and the total electrostatic energy is finite. We obtain
corrections to the Coulomb law at $r\rightarrow\infty$. The weak, dominant and
strong energy conditions are investigated. Magnetized charged black hole is
considered and we evaluate the mass, metric function and their asymptotic at
$r\rightarrow\infty$ and $r\rightarrow 0$. The magnetic mass of the black hole
is calculated. The thermodynamic properties and thermal stability of regular
black holes are discussed. We calculate the Hawking temperature of black holes
and show that there are first-order and second-order phase transitions. The
parameters of the model when the black hole is stable are found.
