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Dexterous robotic hands often struggle to generalize effectively in complex environments due to models trained on low-diversity data. However, the real world presents an inherently unbounded range of scenarios. A natural solution is to enable robots learning from experience in complex environments--an approach akin to evolution, where systems improve through learning from both failures and successes. Motivated by this, we propose EvolvingGrasp, an evolutionary grasp generation method that continuously enhances grasping performance through efficient preference alignment. Specifically, we introduce Handpose-wise Preference Optimization (HPO), which allows the model to continuously align with preferences from both positive and negative feedback while progressively refining its grasping strategies. To further enhance efficiency and reliability during online adjustments, we incorporate a Physics-aware Consistency Model within HPO, which accelerates inference, reduces the number of timesteps needed for preference fine-tuning, and ensures physical plausibility throughout the process. Our results validate that EvolvingGrasp enables evolutionary grasp generation, ensuring robust, physically feasible, and preference-aligned grasping in both simulation and real scenarios.