Inspired by bird wings that enable robust aerodynamic force production and stable flight, we propose a biomimetic blade design for small wind turbines that is capable of achieving a high integral power coefficient, C_p, over a broad range of tip-speed ratios, λ, and hence enhances robustness in aerodynamic performance. We first developed a basic blade design with bird-inspired flexed wing morphology and investigated its aerodynamic characteristics with computational fluid dynamics. Our results demonstrated that the swept-forward shaped portion proximal to wing root augmented C_p at smaller λ, whereas the distal swept-backward shaped portion improved C_p at larger λ. We further conducted a morphology optimization and developed an optimized flexion blade that is capable of achieving a remarkably improved C_p over a broad range of λ. To evaluate the aerodynamic robustness under variable tip-speed ratios in an integral way, we here propose a new Robustness Index (Ri) and find that the optimized-flexion blade outperforms a conventional blade based on Blade Element Momentum Theory by 8.1%, indicating marked robustness in power output. Our results indicate that of great potential for wind turbines robustness-oriented biomimetic blade design can be a practical and effective methodology in wind-based sustainable energy harvesting.