The application of poly(butylene adipate-co-terephthalate) (PBAT) in lightweight applications is hindered by its low melt strength. In this study, isocyanuric triallyl cyanurate (TGIC) was employed to enhance the melt strength of PBAT and improve its foamability under injection molding conditions. The effects of different TGIC contents on the melt crystallization behavior, rheological properties, and mechanical properties of PBAT were studied by differential scanning calorimetry (DSC), rotational rheometer, and universal testing machine. Additionally, scanning electron microscopy (SEM) was used to observe the foaming performance of different PBAT samples after TGIC modification. The results of the study demonstrate that the introduction of an appropriate amount of TGIC leads to the formation of long-chain branching in PBAT, which increases crosslinking degree and decrease the crystallinity, crystallization temperature, and melting temperature of PBAT. Additionally, it results in improved tensile strength but reduced elongation at break. The modified PBAT exhibits higher storage modulus, complex viscosity, and lower loss tangent factor, displaying strain hardening behavior, indicating the improvement of melt elasticity and strength. The foamability tests demonstrate that under injection foaming conditions, the samples containing 4% TGIC exhibits the smallest cell diameter, highest cell density, and uniform cell distribution, demonstrating an ideal cell structure and indicating the successful enhancement of PBAT melt strength and foamability through TGIC chain extension modification.