  We present a theoretical model for CaV$_3$O$_7$: the $1/4$-depleted square
spin-$1/2$ Heisenberg model which includes both the nearest-neighbor coupling
($J$) and the next-nearest-neighbor coupling ($J'$), where $J$ and $J'$ are
antiferromagnetic. Recent experiments of the neutron diffraction by Harashina
et.al. report the magnetic ordering at low temperatures, which may be called as
a stripe phase. It is shown that the observed spin structure is not stable in
the classical theory. By employing the modified spin wave theory, we show that
the stripe phase is stabilized by the quantum fluctuations for $J'/J > 0.69$.
In CaV$_3$O$_7$, the coupling constants are estimated as $J \sim J'$ by
comparing the theoretical and experimental results.
