  The chromatic index $\chi'(G)$ of a graph $G$ is the smallest $k$ for which
$G$ admits an edge $k$-coloring such that any two adjacent edges have distinct
colors. The strong chromatic index $\chi'_s(G)$ of $G$ is the smallest $k$ such
that $G$ has an edge $k$-coloring with the condition that any two edges at
distance at most 2 receive distinct colors. A graph is 1-planar if it can be
drawn in the plane so that each edge is crossed by at most one other edge. In
this paper, we show that every graph $G$ with maximum average degree
$\bar{d}(G)$ has $\chi'_{s}(G)\le (2\bar{d}(G)-1)\chi'(G)$. As a corollary, we
prove that every 1-planar graph $G$ with maximum degree $\Delta$ has
$\chi'_{\rm s}(G)\le 14\Delta$, which improves a result, due to Bensmail et
al., which says that $\chi'_{\rm s}(G)\le 24\Delta$ if $\Delta\ge 56$.
