In this study, we synthesized a water-soluble poly(amic acid-co-imide) (PA-I) from ethylenediaminetetraacetic dianhydride (EDTA) and 2,2′-(ethylenedioxy)bis(ethylamine) that possesses comparable transfection efficiency to that of polyethylenimine (PEI), when prepared in combination with divalent calcium cations. The polycondensation of monomers afforded poly(amic acid) (PA) precursors, and subsequent thermal imidization resulted in the formation of PA-I. At a polymer/DNA ratio (indicated by the molar ratio of nitrogen in the polymer to phosphate in DNA) of 40, complete retardation of the DNA band was observed by gel electrophoresis, indicating the strong association of DNA with PA-I. A zeta potential of −22 mV was recorded for the PA-I polymer solution, and no apparent cytotoxicity was observed at concentrations up to 500 μg·mL
−1
. In the presence of divalent Ca
2+
, the transfection efficiency of PA-I was higher than that of PA, due to the formation of a copolymer/Ca
2+
/DNA polyplex and the reduction in negative charge due to thermal cyclization. Interestingly, a synergistic effect of Ca
2+
and the synthesized copolymer on DNA transfection was observed. The use of Ca
2+
or copolymer alone resulted in unsatisfactory delivery, whereas the formation of three-component polyplexes synergistically increased DNA transfection. Our findings demonstrated that a PA-I/Ca
2+
/DNA polyplex could serve as a promising candidate for gene delivery.