Let K n denote the complete graph on n vertices and G, H be finite graphs without loops or multiple edges. Consider a two-coloring of edges of K n . When a copy of G in the first color, red, or a copy of H in the second color, blue is in K n , we write K n → (G, H). The Ramsey number r(G, H) is defined as the smallest positive integer n such that K n → (G, H). Star critical Ramsey r * (G, H) is defined as the largest value of k such that K r(G,H)−1 ⊔ K 1,k → (G, H). In this paper, we find r * (C n , K m ) for m ≥ 7 and n ≥ (m − 3)(m − 1).