Grafting reactions of maleic anhydride onto poly (lactic acid), PLA, were conducted in a Haake torque rheometer, in presence and absence of dicumyl peroxide as a radical initiator. Hydroxyl end groups of PLA were finalized with succinic anhydride before grafting reactions to control condensation reactions of hydroxyl and carbonyl groups. PLAs grafted with maleic anhydride (PLA-g-MA) were analyzed by scanning exclusion chromatography (SEC) and Fourier transformed infrared spectroscopy measurements. The results show reduction of molecular weight of the PLA when the maleic anhydride was present. Blends of PLA and poly(butylene adipate-co-terephthalate), PBAT, were prepared to evaluated the compatibility when the PLA was modified or not , and when the compatibilizing reactions were conducted in situ. Morphological analysis indicated the better compatibility of the blends obtained in situ than those prepared in two steps (grafting of maleic anhydride onto PLA and blend of PLA-g-MA with PBAT).