  A model of nonlinear electrodynamics with the Lagrangian density ${\cal L} =
-(1/\beta)\arcsin(\beta F_{\mu\nu}F^{\mu\nu}/4)$ is proposed. The scale
invariance and the dual invariance of electromagnetic fields are broken in the
model. In the limit $\beta\rightarrow 0$ one comes to Maxwell's electrodynamics
and the scale and dual invariances are recovered. We investigate the effect of
coupling electromagnetic fields with the gravitational field. The asymptotic
black hole solution is found which is similar to the Reissner-Nordstr\"om
solution. We obtain corrections to Coulomb's law and to the
Reissner-Nordstr\"om solution in the model proposed. The existence of the
regular asymptotic at $r\rightarrow 0$ was demonstrated. The mass of the black
hole is calculated possessing the electromagnetic origin. It was shown that
there are not superluminal fluctuations and principles of causality and
unitarity take place.
