With globalization and increasing immigrant populations, immigration departments face significant work-loads and the challenge of ensuring fairness in decision-making processes. Integrating artificial intelligence offers a promising solution to these challenges. This study investigates the potential of large language models (LLMs),such as GPT-3.5 and GPT-4, in supporting immigration decision-making. Utilizing a mixed-methods approach,this paper conducted discrete choice experiments and in-depth interviews to study LLM decision-making strategies and whether they are fair. Our findings demonstrate that LLMs can align their decision-making with human strategies, emphasizing utility maximization and procedural fairness. Meanwhile, this paper also reveals that while ChatGPT has safeguards to prevent unintentional discrimination, it still exhibits stereotypes and biases concerning nationality and shows preferences toward privileged group. This dual analysis highlights both the potential and limitations of LLMs in automating and enhancing immigration decisions.