The use of non-viral vectors for in vivo gene therapy could drastically increase safety, whilst reducing the cost of preparing the vectors. A promising approach to non-viral vectors makes use of DNA/cationic liposome complexes (lipoplexes) to deliver the genetic material. Here we use coarse-grained molecular dynamics simulations to investigate the molecular mechanism underlying efficient DNA transfer from lipoplexes. Our computational fusion experiments of lipoplexes with endosomal membrane models show two distinct modes of transfection: parallel and perpendicular. In the parallel fusion pathway, DNA aligns with the membrane surface, showing very quick release of genetic material shortly after the initial fusion pore is formed. The perpendicular pathway also leads to transfection, but release is slower. We further show that the composition and size of the lipoplex, as well as the lipid composition of the endosomal membrane, have a significant impact on fusion efficiency in our models.