Electronic transport is investigated in the asymmetric graphene superlattice consisting of a periodic potential structure and a wide potential barrier, which are separated by an internal potential well. Our results show that under a certain condition a pronounced peak occurs in the original transmission gap region, and reveal that such an asymmetric graphene superlattice containing a potential well can be equivalent to a double-barrier structure. Furthermore, the controllable potential depth and width of quantum well have significant effects on the transmission probability and electronic conductance. All these phenomena may lead to applications in various graphene-based electronic devices.