  We study theoretically the electronic states in a $5d$ transition metal oxide
Na$_2$IrO$_3$, in which both the spin-orbit interaction and the electron
correlation play crucial roles. Tight-binding model analysis together with the
fisrt-principles band structure calculation predicts that this material is a
layered quantum spin Hall system. Due to the electron correlation, an
antiferromagnetic order first develops at the edge, and later inside the bulk
at low temperatures.
