A b-coloring of a graph G by k colors is a proper vertex coloring such that each color class contains a color-dominating vertex, that is, a vertex having neighbors in all other k-1 color classes. The b-chromatic number χ_b(G) is the maximum integer k for which G has a b-coloring by k colors. Let C_n^r be the rth power of a cycle of order n. In 2003, Effantin and Kheddouci established the b-chromatic number χ_b(C_n^r) for all values of n and r, except for 2r+3≤n≤3r. For the missing cases they presented the lower bound L:= min {n-r-1,r+1+⌊ n-r-1 / 3⌋} and conjectured that χ_b(C_n^r)=L. In this paper, we determine the exact value on χ_b(C_n^r) for the missing cases. It turns out that χ_b(C_n^r)>L for 2r+3≤n≤2r+3+r-6 / 4.