  We construct exact black hole solutions to Einstein gravity with nonlinear
electrodynamic field. In these solutions, there are in general four parameters.
They are physical mass, electric charge, cosmological constant and the coupling
constant. Due to the presence of coupling constant, these solutions differ
significantly from the Reissner-Nordstrom-de Sitter solution in
Einstein-Maxwell gravity with a cosmological constant. In the first place, some
of them are endowed with a topological defect on angle $\theta$. Secondly, for
the extreme charged black holes, the electric charge can be much larger or much
smaller than the mass by varying the coupling constant. Thirdly, for very large
coupling constant, the radius of event horizon for some black holes approaches
$2M$ regardless of the electric charge. Lastly, some black holes are
asymptotically neither flat nor de Sitter (or anti-de Sitter).
