Abstract: The $b$-coloring of a graph $G$ is a proper vertex coloring, in which every two color classes exists at least one edge. The $b$-chromatic number of a graph $G$ is the largest integer $k$ such that $G$ admits a $b$-coloring with $k$ colors. A graph $G$ is said to be $b$-continuity if and only if for every integer $k$, $\chi(G) \leq k \leq b(G)$, there exists a $b$-coloring with $k$ colors. In this paper, the $b$-continuity of some special Corona graphs is proved by designing the specific coloring scheme according to the structural properties of Corona graphs.

Key words: $b$-coloring, $b$-chromatic number, $b$-continuity, $m$-degree, Corona graph