  An $r$-dynamic $k$-coloring of a graph $G$ is a proper $k$-coloring such that
for any vertex $v$, there are at least $\min\{r, deg_G(v) \}$ distinct colors
in $N_G(v)$. The $r$-dynamic chromatic number $\chi_r^d(G)$ of a graph $G$ is
the least $k$ such that there exists an $r$-dynamic $k$-coloring of $G$. The
list $r$-dynamic chromatic number of a graph $G$ is denoted by $ch_r^d(G)$.
Loeb et al. $[11]$ showed that $ch_3^d(G)\leq 10$ for every planar graph $G$,
and there is a planar graph $G$ with $\chi_3^d(G)= 7$.
  In this paper, we study a special class of planar graphs which have better
upper bounds of $ch_3^d(G)$. We prove that $ch_3^d(G) \leq 6$ if $G$ is a
planar graph which is near-triangulation, where a near-triangulation is a
planar graph whose bounded faces are all 3-cycles.
