Large Language Models (LLMs) have achieved remarkable performance in multiple Natural Language Processing (NLP) tasks. Under the premise that protein sequences constitute the protein language, Protein Language Models(PLMs) have advanced the field of protein engineering. However, as of now, unlike LLMs in NLP, PLMs cannot handle the protein understanding task and the protein generation task simultaneously in the Protein Language Processing (PLP) field. This prompts us to delineate the inherent limitations in current PLMs: (i) the lack of natural language capabilities, (ii) insufficient instruction understanding, and (iii) high training resource demands. To address these challenges, we introduce a training framework to transform any general LLM into a PLM capable of handling multiple PLP tasks. To improve training efficiency, we propose Protein Vocabulary Pruning (PVP) for general LLMs. We construct a multi-task instruction dataset containing 13 million samples with superfamily information, facilitating better modeling of protein sequence-function landscapes. Through these methods, we develop the ProLLaMA model, the first known PLM to handle multiple PLP tasks simultaneously. Experiments show that ProLLaMA achieves state-of-the-art results in the unconditional protein sequence generation task. In the controllable protein sequence generation task, ProLLaMA can design novel proteins with desired functionalities. As for the protein understanding task, ProLLaMA achieves a 62\% exact match rate in superfamily prediction. Codes, model weights, and datasets are available at \url{https://github.com/PKU-YuanGroup/ProLLaMA} and \url{https://huggingface.co/GreatCaptainNemo}.
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