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The length of dominating cycles is usually discussed in control problems. A dominating cycle of a graph G is a cycle C of G such that V ( G ) − V ( C ) is an independent set. In this article, we prove that for any claw-free graph G with δ ( G ) ≥ 2 , the length of longest dominating cycle is at least min { n , 2 | N C 2 ( G ) | − 1 } , where N C 2 ( G ) denotes the vertex set N ( u ) ∪ N ( v ) containing the minimum number of vertices for all vertices u , v with d ( u , v ) = 2 in G .