  For each $ \alpha > 0 $, the $\alpha$-Bloch space is consisting of all
analytic functions $f$ on the unit disk satisfying $ \sup_{|z|<1}
(1-|z|^2)^\alpha |f'(z)| < + \infty.$ In this paper, we consider the following
complex integral operator, namely the $\beta$-Ces\`{a}ro operator
\begin{equation}
  C_\beta(f)(z)=\int_{0}^{z}\frac{f(w)}{w(1-w)^{\beta}}dw \nonumber
\end{equation} and its generalization, acting from the $\alpha$-Bloch space to
itself, where $f(0)=0$ and $\beta\in\mathbb{R}$. We investigate the boundedness
and compactness of the $\beta$-Ces\`{a}ro operators and their generalization.
Also we calculate the essential norm and spectrum of these operators.
