  We study the quantum entanglement and quantum phase transition (QPT) of the
anisotropic spin-1/2 XY model with staggered Dzyaloshinskii-Moriya (DM)
interaction by means of quantum renormalization group method. The scaling of
coupling constants and the critical points of the system are obtained. It is
found that when the number of renormalization group iterations tends to
infinity, the system exhibit a QPT between the spin-fluid and N\'eel phases
which corresponds with two saturated values of the concurrence for a given
value of the strength of DM interaction. The DM interaction can enhance the
entanglement and influence the QPT of the system. To gain further insight, the
first derivative of the entanglement exhibit a nonanalytic behavior at the
critical point and it directly associates with the divergence of the
correlation length. This shows that the correlation length exponent is closely
related to the critical exponent, i.e., the scaling behaviors of the system.
