A biobased heat-triggered shape-memory polymer (HSMP) consisting of polylactide (PLA) and epoxidized natural rubber (ENR) was fabricated by peroxide-induced dynamic vulcanization. The cross-linked ENR phase exhibits a continuous net-like structure embedded in the PLA phase, which is different from a conventional plastic/rubber system having the typical "sea-island" morphology in which vulcanized rubber particles were dispersed in plastic matrix. In situ interfacial compatibilization was confirmed by FTIR analysis. The shape-recovery ratios of the PLA/ENR HSMPs were significantly improved over 90%, compared to that (60-70%) of PLA. The shape fixing and memorizing capability of PLA/ENR HSMPs was realized by the glass transition of the PLA phase: cross-linked ENR continuous phase at rubbery state offered strong recovery driving force, improved interface provided effective stress-transferring during shape recovery, and PLA continuous phase served as a "control-switch" for recovery. The biobased PLA/ENR HSMP could serve as a promising alternative to the traditional materials for intelligent biomedical devices.