  The concept of DP-coloring of a graph is a generalization of list coloring
introduced by Dvo\v{r}\'{a}k and Postle in 2015. Multiple DP-coloring of
graphs, as a generalization of multiple list coloring, was first studied by
Bernshteyn, Kostochka and Zhu in 2019. This paper proves that planar graphs
without 3-cycles and normally adjacent 4-cycles are $(7m, 2m)$-DP-colorable for
every integer $m$. As a consequence, the strong fractional choice number of any
planar graph without 3-cycles and normally adjacent 4-cycles is at most $7/2$.
