The cosmological black holes are black holes living not in an asymptotically flat universe but in an expanding spacetime. They have a rich dynamics especially for their mass and horizon. In this article, we perform a natural step in investigating this new type of black hole: we consider the possibility of a charged cosmological black hole. We derive the general equations of motion governing its dynamics and report a new analytic solution for the special case of the charged Lematre-Tolman-Bondi equations of motion that describe a charged cosmological black hole. We then study various relevant quantities for the characterization of the black hole, such as the C-function, the effect of the charge on the black hole flux, and the nature of the singularity. We also perform numerical investigations to strengthen our results. Finally, we challenge a model of gamma ray burst within our framework.