The behavior of deoxyribonucleic acid (DNA) molecules in confinement is of profound importance in various bioengineering and medical applications. In the present study, all-atom molecular dynamics simulation is utilized to investigate the transition of the double-strand DNA (dsDNA) conformation in the electrolytic nanodroplet. Three typical conformations, i.e., C-shaped, folded S-shaped, and double C-shaped, are observed for different droplet sizes and ionic concentrations. To reveal the physics underlying this phenomenon, the characteristics of the dsDNA molecules, such as the overcharging intensity, the end-to-end distance, the radius of gyration, etc. are analyzed in detail based on the numerical results. It is found that the transition can be ascribed to the buckling of the polymer molecules under the compression due to the confinement of the nanodroplet, and it can be modulated by the ionic concentration in the electrolyte. Generally, nanoscale confinement dominates dsDNA behavior over the electrostatic effects in smaller nanodroplets, while the latter becomes more important for larger nanodroplets. This competition results in the persistence length increasing with the nanodroplet radii. Based on these discussions, a non-dimensional elasto-capillary number μ is proposed to classify the dsDNA conformations into three regions.