  The square of a graph $G$, denoted $G^2$, has the same vertex set as $G$ and
has an edge between two vertices if the distance between them in $G$ is at most
$2$. Thomassen (2018) and Hartke, Jahanbekam and Thomas (2016) proved that
$\chi(G^2) \leq 7$ if $G$ is a subcubic planar graph. A natural question is
whether $\chi_{\ell}(G^2) \leq 7$ or not if $G$ is a subcubic planar graph.
Cranston and Kim (2008) showed that $\chi_{\ell}(G^2) \leq 7$ if $G$ is a
subcubic planar graph of girth at least 7. We prove that $\chi_{\ell}(G^2) \leq
7$ if $G$ is a subcubic planar graph of girth at least 6.
