Hyperbranched poly(acrylic acid-co-3-hydroxypropionate) (PAcHP) was synthesized by base-catalyzed hydrogen transfer polymerization of acrylic acid through one step. The copolymers obtained through solution and bulk polymerization were insoluble in water and all organic solvents tried. Structural and compositional characterizations of hyperbranched PAcHP were performed by using FTIR, solid 13C-NMR, TGA, and titrimetric analysis. Acrylate fraction of the hyperbranched PAcHP obtained via bulk polymerization was determined as 60–65% by comparing TGA curves of hyperbranched PAcHP and pure poly(3-hydroxy propionate) (PHP). However, analytical titration of the same sample revealed that acrylic acid units were about 47.3%. The results obtained from TGA and analytical titration were used to evaluate the chemical structure of the copolymer. Hyperbranched PAcHP exhibited hydrogel properties. Swelling behavior of the copolymer was investigated at a wide pH range and ionic strength. The dynamic swelling profiles of hyperbranched PAcHP exhibited a fast swelling behavior in the first hour and achieved the equilibrium state within 12 h in PBS. Depending on the conditions, the copolymers exhibited swelling ratios up to 2100%. As the copolymer has easily biodegradable propionate and versatile functional acrylic acid units, it can be used as not only biodegradable material in medical applications but also raw material in personal care commodities.