  A lattice QCD calculation of the proton matrix element of the flavor singlet
axial-vector current is reported. Both the connected and disconnected
contributions are calculated, for the latter employing the variant method of
wall source without gauge fixing. From simulations in quenched QCD with the
Wilson quark action on a $16^3\times 20$ lattice at $\beta=5.7$ (the lattice
spacing $a\approx 0.14$fm), we find $\Delta\Sigma=\Delta u+\Delta d+\Delta
s=+0.638(54)-0.347(46)-0.109(30) = +0.18(10)$ with the disconnected
contribution to $\Delta u$ and $\Delta d$ equal to $-0.119(44)$, which is
reasonably consistent with the experiment.
