A series of copolyanhydrides, consisting of 2,3,4,5-tetra-O-acetylgalactaric acid (AGA) and adipic acid (AA) as monomer units, was polymerized. Synthesis of AGA monomer consisted of two steps. First, O-acetylation of galactaric acid secondary hydroxyl groups was performed using acetic anhydride as a reagent. Acetic anhydride was then further used as a reagent in the synthesis of diacetyl mixed anhydride of AGA. Polymerizations were conducted as bulk condensation polymerization at 150 °C. Thermal properties of the copolymers varied depending on monomer composition. Increase in the AGA content had a clear increasing effect on the Tg. A similar increasing effect was observed in Tm. The degree of crystallinity decreased as AGA content increased. There was a slightly lowering tendency in the molecular weights of the obtained polymers when the AGA content in the polymerization mixtures increased. The described synthesis route shows that bio-based aldaric acid monomers are potential candidates for the adjustment of thermal properties of polyanhydrides.