Let $$\vec G$$ be a strongly connected digraph and Q( $$\vec G$$ ) be the signless Laplacian matrix of $$\vec G$$ . The spectral radius of Q( $$\vec G$$ ) is called the signless Lapliacian spectral radius of $$\vec G$$ . Let $${\tilde \infty _1}$$ -digraph and $${\tilde \infty _2}$$ -digraph be two kinds of generalized strongly connected 1-digraphs and let $${\tilde \theta _1}$$ -digraph and $${\tilde \theta _2}$$ -digraph be two kinds of generalized strongly connected µ-digraphs. In this paper, we determine the unique digraph which attains the maximum(or minimum) signless Laplacian spectral radius among all $${\tilde \infty _1}$$ -digraphs and $${\tilde \theta _1}$$ -digraphs. Furthermore, we characterize the extremal digraph which achieves the maximum signless Laplacian spectral radius among $${\tilde \infty _2}$$ -digraphs and $${\tilde \theta _2}$$ -digraphs, respectively.