  Motivated by the violation of Lorentz invariancy in quantum gravity, we study
black hole solutions in gravity's rainbow in context of Einstein gravity
coupled with various models of nonlinear electrodynamics. We regard an energy
dependent spacetime and obtain related metric functions and electric fields. We
show that there is an essential singularity at the origin which is covered with
an event horizon. We also compute the conserved and thermodynamical quantities
and examine the validity of the first law of thermodynamics in the presence of
rainbow functions. Finally, we investigate thermal stability conditions for
these black hole solutions in context of canonical ensemble. We show that
thermodynamical structure of the solutions depends on the choices of
nonlinearity parameters, charge and energy functions.
