Poly(butylene succinate) (PBS) is a biodegradable polymer produced from renewable raw materials and is widely used in the production of packaging materials. Among important features, oxygen permeability is crucial for “breathing” packaging materials (such as packaging for medical devices sterilized with gaseous ethylene oxide). Recently, poly(butylene succinate-dilinolene succinate) (PBS-DLS) copolymers containing long chains of fatty acids and showing excellent elasticity were synthesized. In this work, bio-based polymer blends of PBS and PBS-DLS copolymer with an aliphatic-aromatic poly(butylene terephthalate-butylene adipate) (PBAT) (Ecoflex) were prepared in order to further improve their oxygen permeability while maintaining mechanical stability. PBS and PBS-DLS copolymer containing 90 wt% of hard segments and 10 wt% of soft segments, respectively, were used for blends preparation with 10 wt% of PBAT. The chemical structure was analyzed using infrared spectroscopy and thermal properties were determined with differential scanning calorimetry. The melt flow index and hardness were determined and the mechanical and barrier properties were also examined. Low amount of PBAT did not affect melting temperatures for all tested materials. Importantly, the oxygen permeability of PBS-DLS/PBAT blend was comparable to non-biodegradable high-density polyethylene (HDPE) Tyvek used for medical devices packaging.