  An antiferromagnetic Heisenberg model on a 1/5-depleted two-dimensional
square-lattice, a model of CaV$_4$O$_9$, is investigated by variational Monte
Carlo simulation. A prototype of a trial wave function is made by projecting
out the doubly occupied states from the Schwinger-boson mean-field solution.
Then variational Monte Carlo simulation is performed up to $40 \times 40 $
sites(including $320$ vacant sites). The optimized state has the lowest energy,
$-0.5510J$, ever reported. For this state energies of a dimer bond and a
plaquette bond, staggered magnetization, static structure factor, and
excitation spectrum are calculated. It is shown that the N\'eel order survives
and there is no gap at isotropic coupling.
