The Borodin–Kostochka conjecture says that for a graph G , if Δ ( G ) ≥ 9 , then χ ( G ) ≤ max { Δ ( G ) − 1 , ω ( G ) } . Cranston and Rabern in [SIAM J. Discrete. Math. 27 (2013) 534–549] proved the conjecture holding for K 1 , 3 -free graphs. In this paper, we prove that the conjecture holds for K 1 , 3 ¯ -free graphs, where K 1 , 3 ¯ denotes the complement of K 1 , 3 .