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An $r$-dynamic $k$-coloring of a graph $G$ is a proper $k$-coloring such thatfor any vertex $v$, there are at least $\min\{r,\deg_G(v) \}$ distinct colorsin $N_G(v)$. The $r$-dynamic chromatic number $\chi_r^d(G)$ of a graph $G$ isthe least $k$ such that there exists an $r$-dynamic $k$-coloring of $G$. The{\em list $r$-dynamic chromatic number} of a graph $G$ is denoted by$ch_r^d(G)$. Recently, Loeb et al. [UI] showed that the list $3$-dynamicchromatic number of a planar graph is at most 10. And Cheng et al. [Lai-16]studied the maximum average condition to have $\chi_3^d (G) \leq 4, \ 5$, or$6$. On the other hand, Song et al. [SLW] showed that if $G$ is planar withgirth at least 6, then $\chi_r^d(G)\le r+5$ for any $r\ge 3$.  In this paper, we study list 3-dynamic coloring in terms of maximum averagedegree. We show that $ch^d_3(G) \leq 6$ if $mad(G) < \frac{18}{7}$, $ch^d_3(G)\leq 7$ if $mad(G) < \frac{14}{5}$, and $ch^d_3(G) \leq 8$ if $mad(G) < 3$. Allof the bounds are tight.

List 3-dynamic coloring of graphs with small maximum average degree