The aggregation of DNA molecules induced by cationic polymers is of importance to applications in gene delivery. In this work, we performed a series of umbrella sampling molecular dynamics simulations to calculate the potential of mean force (PMF) between two DNA molecules in the presence of polyethylenimine (PEI) molecules using the weighted histogram analysis method. The distance between the centers of mass of the two DNAs was chosen as the reaction coordinate, and the location and depth of the global minimum in the PMF curve were used to gauge the compactness and stability of the formed aggregate. The effects of PEI to DNA charge ratio (N/P charge ratio) and protonation state of the PEI were investigated. The DNA aggregation was found to be more favorable at higher PEI/DNA charge ratios and higher PEI protonation ratios. As compared with small multivalent ions, PEIs give rise to stronger DNA attraction even with an N/P charge ratio at which the DNAs are overneutralized. The effect of changing the protonation ratio on the compactness of the aggregate is more prominent than changing the N/P charge ratio, while the depth of the PMF well is more strongly influenced by the N/P charge ratio.