The Turán number ex(n, H) of a graph H, is the maximum number of edges in a graph of order n which does not contain H as a subgraph. Let Ex(n, H) denote all H-free graphs on n vertices with ex(n, H) edges. Let P i denote a path consisting of i vertices, and mP i denote m disjoint copies of P i. In this paper, we give the Turán number ex(n, 3P 5) for all positive integers n, which partly solve the conjecture proposed by L. Yuan and X. Zhang [7]. Moreover, we characterize all extremal graphs of 3P 5 denoted by Ex(n, 3P 5).