  An injective edge-coloring $c$ of a graph $G$ is an edge-coloring such that
if $e_1$, $e_2$, and $e_3$ are three consecutive edges in $G$ (they are
consecutive if they form a path or a cycle of length three), then $e_1$ and
$e_3$ receive different colors. The minimum integer $k$ such that, $G$ has an
injective edge-coloring with $k$ colors, is called the injective chromatic
index of $G$ ($\chi'_{\textrm{inj}}(G)$). This parameter was introduced by
Cardoso et \textit{al.} \cite{CCCD} motivated by the Packet Radio Network
problem. They proved that computing $\chi'_{\textrm{inj}}(G)$ of a graph $G$ is
NP-hard. We give new upper bounds for this parameter and we present the
relationships of the injective edge-coloring with other colorings of graphs.
The obtained general bound gives 8 for the injective chromatic index of a
subcubic graph. If the graph is subcubic bipartite we improve this last bound.
We prove that a subcubic bipartite graph has an injective chromatic index
bounded by $6$. We also prove that if $G$ is a subcubic graph with maximum
average degree less than $\frac{7}{3} $ (resp. $\frac{8}{3} $, $3$), then $G$
admits an injective edge-coloring with at most 4 (resp. $6$, $7$) colors.
Moreover, we establish a tight upper bound for subcubic outerplanar graphs.
