The $r$-hued coloring of graphs is a hot topic in graph theory, which can be applied to fields like the communication of multi-agent systems in the optimal reconfiguration of power networks. An $(k,r)$-coloring of $G$ is a proper coloring with $k$ colors such that for every vertex $v$ with degree $d(v)$ in $G$, the color number of the neighbors of $v$ is at least min$\{d(v),r\}$. The smallest integer $k$ such that $G$ has an $(k,r)$-coloring is called the $r$-hued chromatic number and denoted by $\chi_{r}(G)$. In this paper, we study the $r$-hued coloring of Cartesian product of cycle and path, and obtain its $r$-hued chromatic number.