Polyethylenimine-graft-poly(L-lactide-co-glycolide) (PEI-g-PLGA) block copolymers were prepared by a ring-opening polymerization of L-lactide and glycolide using PEI as a macroinitiator and stannous octoate as a catalyst in dimethylformamide at 100 °C. The molecular structure of the block copolymers was evaluated with 1H-NMR, and the molecular weight of the block copolymers was determined with gel permeation chromatography. The thermal properties were investigated using differential scanning calorimetery and thermogravimetric analysis. The zetapotential of the pDNA/copolymer complexes was evaluated with dynamic laser light scattering. Cytotoxicity and gene transfection efficiency of PEI-g-PLGA were tested in vitro using human embryonic kidney 293 cell culture. The pDNA/copolymer complexes (N/P = 10) showed a lower zeta-potential than pDNA/PEI25kDa complex, suggesting the lower toxicity of the pDNA/copolymer complexes. The copolymer composition was found to significantly affect the gene transfection efficiency of the pDNA/copolymer complexes. The copolymers with lower contents of PLGA showed higher gene transfection efficiency. These results indicate that these block copolymers are promising candidates for gene delivery vehicles, featuring good biocompatibility, potential biodegradability, and relatively high gene transfection efficiency.