Flexible memory devices are promising for information storage and data processing applications in portable, wearable, and smart electronics operating under curved conditions. In this work, we realized high-performance flexible ferroelectric capacitors based on Hf_0.5Zr_0.5O₂ (HZO) thin film by depositing a buffer layer of Al₂O₃ on polyimide (PI) substrates using atomic layer deposition (ALD). The flexible ferroelectric HZO films exhibit high remnant polarization (P_r) of 21 µC/cm². Furthermore, deterioration of polarization, retention, and endurance performance was not observed even at a bending radius of 2 mm after 5,000 bending cycles. This work marks a critical step in the development of high-performance flexible HfO₂-based ferroelectric memories for next-generation wearable electronic devices.