A graph G of order nis called a unicyclic graph if Gis connected and the number of edges of G is also n.The signless Laplacian matrix of Gis Q(G)=D(G)+A(G),whereD(G)is the diagonal matrix of its vertex degrees,A(G)is the adjacency matrix,q1(G)≥q2(G)≥…≥qn(G)≥0is the eigenvalues of Q(G) and qn-1(G)is the second smallest eigenvalue and denoted by k(G).LetU(n)be the set of all unicyclic graphs on nvertices.When the order n≥25,the second smallest Q eigenvalue of first three largest n-order graphs in the classU(n)(n≥25)together with the corresponding graphs were obtained.