Let A(G) be the adjacent matrix of G and Q(G) = D(G)+A(G) is the signless Laplacian matrix of G. The signless Laplacian spectral radius of G is the largest eigenvalue of Q(G). In this paper we characterize the graphs with the maximum signless Laplacian spectral radii among the graphs with given vertex connectivity, among the graphs with given number of blocks and among the graphs with given pendant vertices, respectively.