  Based on the Veneziano ghost theory of QCD, we estimate the cosmological
constant $\Lambda$, which is related to the vacuum energy density,
$\rho_{\Lambda}$, by $\Lambda = 8\pi G \rho_{\Lambda}$. In the recent Veneziano
ghost theory $\rho_{\Lambda}$ is given by the absolute value of the product of
the local quark condensate and quark current mass:$\rho_{\Lambda} =
\frac{2N_{f}H}{m_{\eta'}}c |m_{q}<0|:\bar{q}q:|0>|$. By solving Dyson-Schwinger
Equations for a dressed quark propagator, we found the local quark condensate
$<0|:\bar{q}q:|0> \simeq -(235 MeV)^{3}$, the generally accepted value. The
quark current mass is $m_{q} \simeq$ 4.0 Mev. This gives the same result for
$\rho_{\Lambda}$ as found by previous authors, which is somewhat larger than
the observed value. However, when we make use of the nonlocal quark condensate,
$<0|:\bar{q}(x)q(0):|0>= g(x)<0|:\bar{q}q:|0>$, with g(x) estimated from our
previous work, we find $\Lambda$ is in a good agreement with the observations.
