Sunlight readability is a critical requirement for display devices, especially for mobile displays. Anti-reflection (AR) films can greatly improve sunlight readability by reducing the surface reflection. In this work, we demonstrate a broadband moth-eye-like AR surface on a flexible substrate, intended for flexible display applications. The motheye-like nanostructure was fabricated by an imprinting process onto a flexible substrate with a thin hard-coating film. The proposed nanostructure exhibits excellent AR with luminous reflectance <0.23% and haze below 1% with indistinguishable image quality deterioration. A rigorous numerical model is developed to simulate and optimize the optical behaviors. Excellent agreement between the experiment and simulation is obtained. Meanwhile, the nanostructure shows robust mechanical characteristics (pencil hardness >3 H), which is favorable for touch panels. A small bending radius (8 mm) was also demonstrated, which makes the proposed nanostructure applicable for flexible displays. Additionally, a fluoroalkyl coating was applied onto the moth-eye-like surface to improve the hydrophobicity (with a water contact angle >100°). Such a self-cleaning feature helps protect touch panels from dust and fingerprints. The proposed moth-eye-like AR film is expected to find widespread applications for sunlight readable flexible and curved displays.