  The space-time geometry exterior to a new four-dimensional, spherically
symmetric and charged black hole solution that, through a coupling of general
relativity with a non-linear electrodynamics, is everywhere non-singular, for
small $r$ it behaves as a de Sitter metric, and asymptotically it behaves as
the Reissner-Nordstr\"{o}m metric, is considered in order to study the
energy-momentum localization. For the calculation of the energy and momentum
distributions, the Einstein, Landau-Lifshitz, Weinberg and M\o ller
energy-momentum complexes have been applied. The results obtained show that in
all prescriptions the energy depends on the mass $M$ of the black hole, the
charge $q$, two parameters $% a\in \mathbb{Z}^+$ and $\gamma\in \mathbb{R}^+$,
and on the radial coordinate $r$. The calculations performed in each
prescription show that all the momenta vanish. Additionally, some limiting and
particular cases for $r$ and $q$ are studied, and a possible connection with
strong gravitational lensing and micro lensing is attempted.
