The present paper investigates the spin- XX model with three-spin interaction (TSI) from a view point of bipartite entanglement. The three-spin system is initially chosen by well-known W entangled state. By analyzing the time-dependency of the concurrence between the nearest and the next-nearest neighbor pair of spins, we show that where the quantum phase transition (QPT) of the infinite-size system might happen can be observed, even from short-time dynamics of such a finite spin system. Manuscript profile