  Motivated by the recent studies of the novel asymptotically global AdS$_4$
black hole with deforming horizon, we consider the action of Einstein-Maxwell
gravity in AdS spacetime and construct the charged deforming AdS black holes
with differential boundary. In contrast to deforming black hole without charge,
there exists at least one value of horizon for an arbitrary temperature. The
extremum of temperature is determined by charge $q$ and divides the range of
temperature into several parts. Moreover, we use an isometric embedding in the
three-dimensional space to investigate the horizon geometry. We also study the
entropy and quasinormal modes of deforming charged AdS black hole. It is
interesting to find there exist two families of black hole solutions with
different horizon radius for a fixed temperature, but these two black holes
have same horizon geometry and entropy. Due to the existence of charge $q$, the
phase diagram of entropy is more complicated.
