This talk shows that an entanglement analysis for a pair of spins may be a powerful tool for understanding quantum phase transition(QPT) of one-dimensional quantum spin system (Ising model and XY model under transverse magnetic field). In particuler, the Lewenstein-Sanpera decomposition of a two-qubit density matrix provides us with a clear understanding of the behavior of entanglement undergoing QPT. Around the QPT point, on the basis of L-S decomposition, we can observe the singular maximization of quantum spin fluctuation and the divergence in the spin correlation length.