Attribute-based Zero-Shot Learning (ZSL) has revolutionized the ability of models to recognize new classes not seen during training. However, with the advancement of large-scale models, the expectations have risen. Beyond merely achieving zero-shot generalization, there is a growing demand for universal models that can continually evolve in expert domains using unlabeled data. To address this, we introduce a scaled-down instantiation of this challenge: Evolutionary Generalized Zero-Shot Learning (EGZSL). This setting allows a low-performing zero-shot model to adapt to the test data stream and evolve online. We elaborate on three challenges of this special task, \ie, catastrophic forgetting, initial prediction bias, and evolutionary data class bias. Moreover, we propose targeted solutions for each challenge, resulting in a generic method capable of continuous evolution from a given initial IGZSL model. Experiments on three popular GZSL benchmark datasets demonstrate that our model can learn from the test data stream while other baselines fail. Codes are available at \url{https://github.com/cdb342/EGZSL}.