  In the first part of this article, we proved a local version of the circular
law up to the finest scale $N^{-1/2+ \e}$ for non-Hermitian random matrices at
any point $z \in \C$ with $||z| - 1| > c $ for any $c>0$ independent of the
size of the matrix. Under the main assumption that the first three moments of
the matrix elements match those of a standard Gaussian random variable after
proper rescaling, we extend this result to include the edge case $
|z|-1=\oo(1)$. Without the vanishing third moment assumption, we prove that the
circular law is valid near the spectral edge $ |z|-1=\oo(1)$ up to scale
$N^{-1/4+ \e}$.
