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Protein engineering faces challenges in finding optimal mutants from a massive pool of candidate mutants. In this study, we introduce a deep-learning-based data-efficient fitness prediction tool to steer protein engineering. Our methodology establishes a lightweight graph neural network scheme for protein structures, which efficiently analyzes the microenvironment of amino acids in wild-type proteins and reconstructs the distribution of the amino acid sequences that are more likely to pass natural selection. This distribution serves as a general guidance for scoring proteins toward arbitrary properties on any order of mutations. Our proposed solution undergoes extensive wet-lab experimental validation spanning diverse physicochemical properties of various proteins, including fluorescence intensity, antigen-antibody affinity, thermostability, and DNA cleavage activity. More than 40% of ProtLGN-designed single-site mutants outperform their wild-type counterparts across all studied proteins and targeted properties. More importantly, our model can bypass the negative epistatic effect to combine single mutation sites and form deep mutants with up to seven mutation sites in a single round, whose physicochemical properties are significantly improved. This observation provides compelling evidence of the structure-based model's potential to guide deep mutations in protein engineering. Overall, our approach emerges as a versatile tool for protein engineering, benefiting both the computational and bioengineering communities.