Starch, as an inexpensive natural polymer, can be used as a filler to effectively reduce the cost of poly(butylene adipate-co-terephthalate) (PBAT) products. In this work, corn starch, glycerol, initiator bis(1-(tert-butylperoxy)-1-methylethyl)-benzene and crosslinker 1,3,5-tri-2-propenyl-1,3,5-triazine-2,4,6(1H,3H,5H)-trione (TAIC) were first mixed and extruded into crosslinkable thermoplastic starch (TPS). Then, TPS and PBAT were melt-blended to prepare PBAT/TPS composites. Finally, the PBAT/TPS composites were blow molded into films. The effects of different TAIC contents on the degree of gelation, morphological structure, and properties of the composite films were explored. The results showed that TAIC as a crosslinking agent could improve the mechanical properties of the composite films and increase the compatibility of TPS and PBAT. When the content of TAIC was 2 wt % of TPS, and the TPS content was 30 wt %, the composite film exhibited a tensile strength of 25.43 MPa and elongation at break of 580.83%, along with good processing and degradation properties. The significant improvement in mechanical properties was primarily attributed to TAIC crosslinking the TPS and co-crosslinking the TPS and PBAT interface, enhancing their compatibility. The dynamic vulcanization process provided a simple yet effective approach to prepare inexpensive biodegradable composite films with excellent mechanical properties.