  We consider a mass conserved Allen-Cahn equation $u_t=\Delta u+ \e^{-2}
(f(u)-\e\lambda(t))$ in a bounded domain with no flux boundary condition, where
$\e\lambda(t)$ is the average of $f(u(\cdot,t))$ and $-f$ is the derivative of
a double equal well potential. Given a smooth hypersurface $\gamma_0$ contained
in the domain, we show that the solution $u^\e$ with appropriate initial data
approaches, as $\e\searrow0$, to a limit which takes only two values, with the
jump occurring at the hypersurface obtained from the volume preserving mean
curvature flow starting from $\gamma_0$.
