Polyamidoamine (PAMAM) dednrimer bearing a well-defined number of amine groups can be protonated under physiological or acidic condition to generate the macrocations capable of forming electrostatic complex (called "dendriplex") with DNA for gene delivery. Using small-angle X-ray scattering (SAXS) and small angle neutron c scattering (SANS), here we constructed the morphological map of the complex of DNA with PAMAM dendrimer of generation four (G4) in terms of the dendrimer charge density and the nominal N/P ratio given by the feed molar ratio of dendrimer amine group to DNA phosphate group. With the increase of dendrimer charge density under a given nominal N/P ratio, the structure was found to transform from square columnar phase (in which the DNA chains packed in square lattice were locally straightened) to hexagonally-packed DNA superhelices (in which the DNA chains organizing in a hexagonal lattice twisted moderately into superhelices) and finally to beads-on-string structure (in which DNA wrapped around the dendrimer to form nuclesome-like array). The phase transition sequence was understood from the balance between the bending energy of DNA and the free energy of charge matching governed by the entropic gain from counterion release. Decreasing the nominal N/P ratio under fixed dendrimer charge density was found to exert the same effect as increasing dendrimer charge density; that is, the structure with higher DNA curvature tended to form at a lower nominal N/P ratio, in particular for the dendriplex with low dendrimer charge density. The effect of the N/P ratio was attributed to the tendency of the system to increase the translational entropy of the counterions released to the bulk solution by reducing the concentration of free DNA or dendrimer remained in the solution. The experimental results presented here thus demonstrated the crucial role of counterion entropy in the structural formation of DNA-dendrimer complexes, and this entropic contribution was governed by the dendrimer charge density, the nominal N/P ratio, and the initial concentrations of DNA and dendrimer used for complex preparation.