  A Berge-path of length $k$ in a hypergraph $\mathcal{H}$ is a sequence
$v_1,e_1,v_2,e_2,\dots,v_{k},e_k,v_{k+1}$ of distinct vertices and hyperedges
with $v_{i},v_{i+1} \in e_i$, for $i \le k$. F\"uredi, Kostochka and Luo, and
independently Gy\H{o}ri, Salia and Zamora determined the maximum number of
hyperedges in an $n$-vertex, connected, $r$-uniform hypergraph that does not
contain a Berge-path of length $k$ provided $k$ is large enough compared to
$r$. They also determined the unique extremal hypergraph $\mathcal{H}_1$.
  We prove a stability version of this result by presenting another
construction $\mathcal{H}_2$ and showing that any $n$-vertex, connected,
$r$-uniform hypergraph without a Berge-path of length $k$, that contains more
than $|\mathcal{H}_2|$ hyperedges must be a sub-hypergraph of the extremal
hypergraph $\mathcal{H}_1$, provided $k$ is large enough compared to $r$.
