  We investigate entanglement and quantum phase transition (QPT) in a
two-dimensional Heisenberg anisotropic spin-1/2 XY model, using quantum
renormalization group method (QRG) on a square lattice of $N\times N$ sites.
The entanglement through geometric average of concurrences is calculated after
each step of the QRG. We show that the concurrence achieves a non zero value at
the critical point more rapidly as compared to one-dimensional case. The
relationship between the entanglement and the quantum phase transition is
studied. The evolution of entanglement develops two saturated values
corresponding to two different phases. We compute the first derivative of the
concurrence, which is found to be discontinuous at the critical point
$\gamma=0$, and indicates a second-order phase transition in the spin system.
Further, the scaling behaviour of the system is investigated by computing the
first derivative of the concurrence in terms of the system size.
