  We study if eternal inflation is realized while satisfying the recently
proposed string Swampland criteria concerning the range of scalar field
excursion, $|\Delta \phi| < \mathcal{D} \cdot M_{\rm P}$, and the potential
gradient, $|\nabla V| > c \cdot V/M_{\rm P}$, where $\mathcal{D}$ and $c$ are
constants of order unity, and $M_{\rm P}$ is the reduced Planck mass. We find
that only the eternal inflation of chaotic type is possible for $c \sim {\cal
O}(0.01)$ and $1/\mathcal{D} \sim {\cal O}(0.01)$, and that the Hubble
parameter during the eternal inflation is parametrically close to the Planck
scale, and is in the range of $2 \pi c \lesssim H_{\rm inf}/M_{\rm P} <
1/\sqrt{3}$.
