  We generalize a result of Balister, Gy{\H{o}}ri, Lehel and Schelp for
hypergraphs. We determine the unique extremal structure of an $n$-vertex,
$r$-uniform, connected, hypergraph with the maximum number of hyperedges,
without a $k$-Berge-path, where $n \geq N_{k,r}$, $k\geq 2r+13>17$.
