The behavior of long DNA molecules in a cell-sized confined space was investigated. We prepared water-in-oil droplets covered by phospholipids, which mimic the inner space of a cell, following the encapsulation of DNA molecules with unfolded coil and folded globule conformations. Microscopic observation revealed that the adsorption of coiled DNA onto the membrane surface depended on the size of the vesicular space. Globular DNA showed a cell-size-dependent unfolding transition after adsorption on the membrane. Furthermore, when DNA interacted with a two-phase membrane surface, DNA selectively adsorbed on the membrane phase, such as an ordered or disordered phase, depending on its conformation. We discuss the mechanism of these trends by considering the free energy of DNA together with a polyamine in the solution. The free energy of our model was consistent with the present experimental data. The cooperative interaction of DNA and polyamines with a membrane surface leads to the size-dependent behavior of molecular systems in a small space. These findings may contribute to a better understanding of the physical mechanism of molecular events and reactions inside a cell.