Abstract: In this note, we introduce and study a new kind of generalized Cesàro operator, $\mathcal{C}_{\mu}$, induced by a positive Borel measure $\mu$ on $[0, 1)$ between 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, $\mathcal{D}_{\beta}$.

Key words: generalized Cesàro operator, Dirichlet-type spaces, Carleson measure, boundedness and compactness of operator