From the point of better biocompatibility and sustainability, biobased shape memory polymers (SMPs) are highly desired. We used 1,3-propanediol, sebacic acid, and itaconic acid, which have been industrially produced via fermentation or extraction with large quantities as the main raw materials for the synthesis of biobased poly(propylene sebacate). Diethylene glycol was used to tailor the flexibility of the polyester. The resulted polyesters were found to be promising SMPs with excellent shape recovery and fixity (near 100% and independent of thermomechanical cycles). The switching temperature and recovery speed of the SMPs are tunable by controlling the composition of the polyesters and their curing extent. The continuously changed switching temperature ranging from 12 to 54 °C was realized. Such temperature range is typical for biomedical applications in the human body. The molecular and crystalline structures were explored to correlate to the shape memory behavior. The combination of potential biocompatibility and biodegradability of the biobased SMPs makes them suitable for fabricating biomedical devices.