A series of all-atom molecular dynamics (MD) simulations of the complexation between DNA and 2 kDa branched and linear polyethylenimines (PEIs) are reported in this study. The simulations revealed distinct binding modes of branched and linear PEIs to DNA, with branched PEIs adhering to the DNA surface like beads and linear PEIs adhering to the DNA surface like cords. The dynamics of each PEI's binding state to the DNA during the simulations and how the PEIs neutralize the DNA were quantified. For both branched and linear PEIs, the addition of salt ions similar to physiological conditions were found to have only a small effect on DNA/PEI complexation compared to salt-free conditions. The simulation results reported here will be helpful to understand the mechanism of action for the PEI-based gene carriers.