  We present a new family of topological charged hairy black hole solutions in
asymptotically AdS space in $D$-dimensions. We solve the coupled
Einstein-Maxwell-Scalar gravity system and obtain exact charged hairy black
hole solutions with planar, spherical and hyperbolic horizon topologies. The
scalar field is regular everywhere. We discuss the thermodynamics of the hairy
black hole and find drastic changes in its thermodynamic structure due to the
scalar field. For the case of planar and spherical horizons, we find charged
hairy/RN-AdS black hole phase transition, with thermodynamically preferred and
stable charged hairy phases at low temperature. For the case of hyperbolic
horizon, no such transition occurs and RN-AdS black holes are always
thermodynamically favoured.
