Development of efficient delivery systems is a constraint on the delivery of messenger RNA (mRNA). In gene therapy, it is crucial that mRNA molecules are efficiently delivered into cells. The thesis study has focused on the development of a relatively new polymer, P(OEGMA)-b-P(AEAEMA) as a new mRNA delivery system. P(OEGMA)-b-P(AEAEMA) block copolymers with changing block lengths (P(OEGMA)42-b-P(AEAEMA)48 and P(OEGMA)42-b-P(AEAEMA)71) were first synthesized via RAFT polymerization. The synthesized block copolymers efficiently complexed with eGFP encoded mRNA as shown by gel electrophoresis. The hydrodynamic size of polyplexes was less than 150 nm, as determined by dynamic light scattering measurements. Zeta potential measurements showed that the surface charge of the polymer-mRNA complexes was slightly negative. The eGFP-encoding mRNA transfection ability of the copolymers was investigated via fluorescence microscopy and Image J analyses. The block copolymers showed mRNA transfection efficiency on human embryonic kidney (HEK293T) and mouse fibroblast (L929) cell lines higher than the golden standard polymer, branched PEI. P(OEGMA)42-b-P(AEAEMA)48 and P(OEGMA)42-b-P(AEAEMA)71 showed a transfection efficiency of 54 and 64% of the positive control (cells transfected with Lipofectamine-mRNA complexes), respectively, on human embryonic kidney (HEK293T) cell line. On mouse fibroblast (L929) cell line, P(OEGMA)42-b-P(AEAEMA)48 and P(OEGMA)42-b-P(AEAEMA)71 block copolymers showed a transfection efficiency of 61 and 56% of the positive control, respectively. The polymer complexes showed tolerable (>70%) or no cytotoxicity on the cells in the tested range. In summary, P(OEGMA)-b-P(AEAEMA) block copolymers have shown promising mRNA transfection ability on both HEK293T and L929 cell lines.