  In this note, we introduce and study a new kind of generalized Ces\`aro
operators $\mathcal{C}_{\mu}$, induced by a positive Borel measure $\mu$ on
$[0, 1)$, between the Dirichlet-type spaces. We characterize the measures $\mu$
for which $\mathcal{C}_{\mu}$ is bounded (compact) from one Dirichlet-type
space $\mathcal{D}_{\alpha}$ into another one $\mathcal{D}_{\beta}$.
