Protein evolution through amino acid mutations is a cornerstone of life sciences. Recent advances in protein language models have shown rich evolutionary patterns, offering unprecedented potential for in-silicon directed evolution. However, existing directed evolution methods largely rely on heuristic evolution strategies and have yet to efficiently integrate the transformative protein language models with advanced optimization techniques, such as reinforcement learning, to adaptively learn superior evolution policies. To bridge this gap, we propose AlphaDE, a novel framework that evolves protein sequences by harnessing the innovative paradigms of large language models, such as fine-tuning and test-time inference. First, AlphaDE fine-tunes pretrained protein language models using masked language modeling on homologous protein sequences to activate the evolutionary plausibility of the interested protein family. Second, AlphaDE introduces test-time inference based on Monte Carlo tree search, which effectively evolves proteins with evolutionary guidance from the fine-tuned protein language model. Extensive benchmark experiments show that AlphaDE remarkably outperforms previous state-of-the-art methods even with few-shot fine-tuning. A case study further demonstrates that AlphaDE supports condensing the protein sequence space of avGFP through computational evolution.