  A graph is outer-1-planar if it can be drawn in the plane so that all
vertices are on the outer face and each edge is crossed at most once. It is
known that the list edge chromatic number $\chi'_l(G)$ of any outer-1-planar
graph $G$ with maximum degree $\Delta(G)\geq 5$ is exactly its maximum degree.
In this paper, we prove $\chi'_l(G)=\Delta(G)$ for outer-1-planar graphs $G$
with $\Delta(G)=4$ and with the crossing distance being at least 3.
