A barite filter cake removing composition, and single- and multi-stage methods of removing a barite filter cake from a wellbore. The composition comprises at least one polymer removal agent, at least one chelating agent, and at least one converting agent. The single-stage method includes contacting the barite filter cake with the composition to dissolve the barite filter cake from the wellbore. The multi-stage method includes contacting the barite filter cake from the wellbore with at least one polymer removal agent to remove a polymer coat present on the barite filter cake, contacting the barite filter cake with at least one converting agent to convert barium sulfate in the barite filter cake to a barium salt of carbonate, formate, cyanide, nitrate, and/or chloride, and removing the barium salt of carbonate, formate, cyanide, nitrate, and/or chloride with at least one chelating agent.