This original research developed active polylactic acid (PLA) film strips for use inside food packaging to extend the shelf-life of bananas (Musa AAA group). Multibranched PLA functionalized with gallic acid (GA) (mPLA-GA) was prepared by ring-opening polymerization and functionalization. mPLA-GA was compounded with PLA and fabricated into PLA/mPLA-GA film strips by melt processing using different mPLA-GA contents (1, 2 and 4 wt%). The morphology, antioxidant activity, free-radical scavenging ability under a radiation sterilization dose (25 kGy), migration behavior, mechanical properties, and O2 scavenging capacity of PLA/mPLA-GA film strips were determined and compared with neat PLA and PLA/GA film strips. Bananas were vacuum-packed using commercial plastic packaging together with the PLA-based film strips and kept at room temperature for 14 days. The performance of the PLA/mPLA-GA film strips in extending the shelf-life of bananas was investigated by physical appearance, peel color difference (ΔE*ab), ripening index (RI), and firmness. Analysis of variance at the 0.05 level of significance (p ≤ 0.05) was conducted to compare mean values. PLA/mPLA-GA film strips exhibited a homogeneous matrix with improved mechanical properties and showed outstanding antioxidant as well as O2 scavenging effects by preventing the bloating of packaging, delaying fruit ripening, and extending the shelf-life of bananas. Under vacuum packaging with PLA/mPLA-GA film strips, bananas retained their green peel color and firmness after storing for 14 days. The results suggest that PLA/mPLA-GA film strips show promise as an active bioplastic for extending the shelf-life of bananas as well as other fruits and food items.