The inadequate rheological properties limit the film blowing process of biodegradable polylactic acid (PLA), thus hindering its potential application in environmentally friendly packaging films and mulch films. Herein, biodegradable polyethylene glycol (PEG) and d-lactide were used to synthesize three kinds of poly-d-lactic acid (PDLA)-b-PEG-b-PDLA (DPD) triblock copolymers, and their effects on stereocomplex (sc) structure formation and rheological properties of the composites were studied. The results showed that the poly l-lactic acid (PLLA)/DPD4k sample introduced the highest sc content, storage modulus, and complex viscosity value compared with PLLA/DPD2k and PLLA/DPD10k at the same loading condition, indicating that the PEG4k chains can better accelerate the formation of a sc network between DPD4k and the PLLA matrix. The introduction of 10 wt % DPD4k also resulted in about 38 times longer relaxation time and a strain-hardening behavior during the steady biaxial extension of PLLA. At last, the continuous film blowing process was successfully conducted in the PLLA/DPD4k composites, which acquired a stable blow-up ratio of 3.07. On the basis of the above results, the soft chain-grafted PDLA copolymer may provide a novel method for film blowing of biodegradable PLA.