The purposes of this article is to establish some necessary and sufficient conditions for the boundedness of the rough Hausdorff operators on weighted Herz, central Morrey and Morrey–Herz spaces on the Heisenberg group. By applying the block decomposition method, the authors also obtain the boundedness of the rough Hausdorff operators on weighted Herz spaces for the case p 2 ð0; 1Þ.