  In this paper, we study a non-collapsed Gromov--Hausdorff limit of a sequence
of compact Heisenberg manifolds with sub-Riemannian metrics. In the case of
strictly sub-Riemannian case, we show that if a sequence has an upper bound of
the diameter and a lower bound of Popp's measure, then it has a convergent
subsequence in the Gromov--Hausdorff topology, and the limit is isometric to a
compact Heisenberg manifold of the same dimension. The same conclusion is also
shown for Riemannian case with the additional assumption on Ricci curvature
lower bounds.
