  The energy-momentum of a new four-dimensional, charged, spherically symmetric
and nonsingular black hole solution constructed in the context of general
relativity coupled to a theory of nonlinear electrodynamics is investigated,
whereby the nonlinear mass function is inspired by the probability density
function of the continuous logistic distribution. The energy and momentum
distributions are calculated by use of the Einstein, Landau-Lifshitz, Weinberg
and M{\o}ller energy-momentum complexes. In all these prescriptions it is found
that the energy distribution depends on the mass $M$ and the charge $q$ of the
black hole, an additional parameter $\beta$ coming from the gravitational
background considered, and on the radial coordinate $r$. Further, the
Landau-Lifshitz and Weinberg prescriptions yield the same result for the
energy, while in all the aforesaid prescriptions all the momenta vanish. We
also focus on the study of the limiting behavior of the energy for different
values of the radial coordinate, the parameter $\beta$, and the charge $q$.
Finally, it is pointed out that for $r\rightarrow \infty$ and $q = 0$ all the
energy-momentum complexes yield the same expression for the energy distribution
as in the case of the Schwarzschild black hole solution.
