For a simple graph $G$, an adjacent vertex distinguishing (or AVD) total $k$-coloring is a proper total $k$-coloring of $G$ such that any two adjacent vertices have different color sets; a color set for vertex $v$ consisting of the color of $v$ and the colors of its incidence edges. The AVD total chromatic number $\chi_a''(G)$ is the minimum $k$ such that $G$ has an AVD total $k$-coloring. Here is the main result. \par Theorem. For any planar graph $G$ with maximum degree $\Delta(G) $, $\chi_a''(G)\leq \max\{\Delta(G) + 2, 12\}$. \par Moreover, any planar graph $G$ with maximum degree 10 has an AVD total-$(\Delta(G)+2)$-coloring and the bound $\Delta(G)+2$ is sharp.