In this paper we investigate some new sufficient conditions for a digraphs D with covering number θ(D)≤3 to be kernel perfect(KP). Let D be a digraph with θ(D)≤3 such that every directed triangle is symmetrical.In this paper we prove the following two results: (1)If every directed cycle of length 4 has two symmetrical arcs and every directed cycle of length 5 has one diagonal or two symmetrical arcs

then D is a kernel perfect graph. (2)If every directed cycle of length 5 has two symmetrical arcs and one diagonal

then D is a kernel perfect graph.