Let G be a simple, connected graph, D ( G ) be the distance matrix of G , and Tr ( G ) be the diagonal matrix of vertex transmissions of G . The distance signless Laplacian matrix of G is defined as D Q ( G ) = T r ( G ) + D ( G ) , and the distance signless Laplacian spectral radius of G is the largest eigenvalue of D Q ( G ) . In this paper, we study Nordhaus–Gaddum-type inequalities for distance signless Laplacian eigenvalues of graphs and present some new upper and lower bounds on the distance signless Laplacian spectral radius of G and of its line graph L ( G ), based on other graph-theoretic parameters, and characterize the extremal graphs. Further, we study the distance signless Laplacian spectrum of some graphs obtained by operations.