  Extensions of Erd\H{o}s-Gallai Theorem for general hypergraphs are well
studied. In this work, we prove the extension of Erd\H{o}s-Gallai Theorem for
linear hypergraphs. In particular, we show that the number of hyperedges in an
$n$-vertex $3$-uniform linear hypergraph, without a Berge path of length $k$ as
a subgraph is at most $\frac{(k-1)}{6}n$ for $k\geq 4$.
