Computational protein design (CPD) offers transformative potential for bioengineering, but current deep CPD models, focused on universal domains, struggle with function-specific designs. This work introduces a novel CPD paradigm tailored for functional design tasks, particularly for enzymes-a key protein class often lacking specific application efficiency. To address structural data scarcity, we present CrossDesign, a domain-adaptive framework that leverages pretrained protein language models (PPLMs). By aligning protein structures with sequences, CrossDesign transfers pretrained knowledge to structure models, overcoming the limitations of limited structural data. The framework combines autoregressive (AR) and non-autoregressive (NAR) states in its encoder-decoder architecture, applying it to enzyme datasets and pan-proteins. Experimental results highlight CrossDesign's superior performance and robustness, especially with out-of-domain enzymes. Additionally, the model excels in fitness prediction when tested on large-scale mutation data, showcasing its stability.