  Let $g$ be a holomorphic map of $B$, where $B$ is the unit ball of ${C}^n$.
Let $0<p<+\infty, -n-1<q<+\infty$, $q>-1$ and $\alpha>0$. This paper gives some
necessary and sufficient conditions for the Extended Ces$\acute{a}$ro Operators
induced by $g$ to be bounded or compact between generalized Besov space
$B(p,q)$ and $\alpha$- Bloch space ${\mathcal B}^\alpha.$
