The dispersion of the nanometer-sized carbon nanotubes in a polymer matrix leads to a marked improvement in the properties of the polymer. This approach can also be applied to biodegradable synthetic aliphatic polyesters such as poly( l-lactide) (PLLA), which has received a great deal of attention due to environmental concerns. In this study, PLLA was melt compounded with multiwalled carbon nanotubes (MWCNTs). A high degree of dispersion of the MWCNTs in the composites was obtained by grafting PLLA onto the MWCNTs (PLLA-g-MWCNTs). After oxidizing the MWCNTs by treating them with strong acids, they were reacted with l-lactide to produce the PLLA-g-MWCNTs. The morphology of the composite was observed with scanning electron microscopy. The mechanical properties of the PLLA/PLLA-g-MWCNT composite were higher than those of the PLLA/MWCNT composite. The thermal stability of the composites was studied using thermogravimetric analysis and their activation energy during thermal degradation was determined using the Kissinger and Flynn–Wall–Ozawa methods. The activation energy of PLLA/PLLA-g-MWCNT was higher than that of PLLA/MWCNT, which indicates that the composite made with the PLLA-g-MWCNTs was more thermally stable than the composite made with the MWCNTs.