  In this work a study about the energy-momentum of a new four-dimensional
spherically symmetric, static and charged, regular black hole solution
developed in the context of general relativity coupled to nonlinear
electrodynamics is presented. Asymptotically, this new black hole solution
behaves as the Reissner-Nordstr\"om solution only for the particular value
{\mu}=4, where {\mu} is a positive integer parameter appearing in the mass
function of the solution. The calculations are performed by use of the
Einstein, Landau-Lifshitz, Weinberg and M{\o}ller energy-momentum complexes. In
all the aforesaid prescriptions, the expressions for the energy of the
gravitating system considered depend on the mass M of the black hole, its
charge q, a positive integer {\alpha} and the radial coordinate r. In all these
pseudotensorial prescriptions the momenta are found to vanish, while the
Landau-Lifshitz and Weinberg prescriptions give the same result for the energy
distribution. In addition, the limiting behavior of the energy for the cases r
tends toward infinity, r=0 and q=0 is studied. The special case {\mu}=4 and
{\alpha}=3 is also examined. We conclude that the Einstein and M{\o}ller
energy-momentum complexes can be considered as the most reliable tools for the
study of the energy-momentum localization of a gravitating system.
