  In this work, we consider that in energy scales greater than the Planck
energy, the geometry, fundamental physical constants, as charge, mass, speed of
light and Newtonian constant of gravitation, and matter fields will depend on
the scale. This type of theory is known as Rainbow Gravity. We coupled the
nonlinear electrodynamics to the Rainbow Gravity, defining a new mass function
$M(r,\epsilon)$, such that we may formulate new classes of spherically
symmetric regular black hole solutions, where the curvature invariants are
well-behaved in all spacetime. The main differences between the General
Relativity and our results in the the Rainbow gravity are: a) The intensity of
the electric field is inversely proportional to the energy scale. The higher
the energy scale, the lower the electric field intensity; b) the region where
the strong energy condition (SEC) is violated decrease as the energy scale
increase. The higher the energy scale, closer to the radial coordinate origin
SEC is violated.
