The biodegradability and mechanical and thermal properties of composites of maleic anhydride-grafted polybutylene succinate (PBSU-g-MA) and agricultural residue (wheat bran, WB) were evaluated. Composites of PBSU-g-MA and WB (PBSU-g-MA/WB) exhibited superior mechanical properties compared to PBSU/WB due to better compatibility. The dispersion of WB in the PBSU-g-MA matrix was highly homogeneous due to ester formation between the anhydride groups of PBSU-g-MA and the hydroxyl groups of WB, which resulted in the formation of branched, crosslinked macromolecules. PBSU-g-MA/WB composites were more easily processed due to their lower melt viscosity. They also showed better water resistance, although both composites were biodegradable, especially at higher levels of WB substitution. Both composites were more biodegradable than pure PBSU, implying a strong connection between WB content and biodegradability.