The resistance distance between any two vertices of a connected graph G is defined as the effective resistance between them in the electrical network constructed from G by replacing each edge of G with unit resistor. The Kirchhoff index of a graph G is defined as the sum of the resistance distances between all pairs of vertices of G. L-n,L-p* denote a specified class of graphs with n vertices, which obtained by identifying the vertex u(i) of the complete graph K-p with the root v(i) of the tree T-i, respectively, where i=1,2, ... ,r and 1 <= r <= p. We obtain some ordering relations of Kirchhoff indices for four graph transformations, and thus determine the graphs with the first-smallest to the fifth-smallest Kirchhoff indices as well as the maximal Kirchhoff index of L-n,L-p*, respectively.