Let G be a strongly connected digraph with distance matrix D(G) and let Tr(G) be the diagonal matrix with vertex transmissions of G. For any real α ∈ [0, 1], define the matrix D α (G) as D α (G) = αTr(G) + (1 − α)D(G). The D α spectral radius of G is the spectral radius of D α (G). In this paper, we first give some upper and lower bounds for the D α spectral radius of G and characterize the extremal digraphs. Moreover, for digraphs that are not transmission regular, we give a lower bound on the difference between the maximum vertex transmission and the D α spectral radius. Finally, we obtain the D α eigenvalues of the join of certain regular digraphs