  A graph $G$ contains another graph $H$ as an immersion if $H$ can be obtained
from a subgraph of $G$ by splitting off edges and removing isolated vertices.
In this paper, we prove an edge-variant of the Erd\H{o}s-P\'{o}sa property with
respect to the immersion containment in 4-edge-connected graphs. More
precisely, we prove that for every graph $H$, there exists a function $f$ such
that for every 4-edge-connected graph $G$, either $G$ contains $k$ pairwise
edge-disjoint subgraphs each containing $H$ as an immersion, or there exists a
set of at most $f(k)$ edges of $G$ intersecting all such subgraphs. This
theorem is best possible in the sense that the 4-edge-connectivity cannot be
replaced by the 3-edge-connectivity.
