Person-Job Fit (PJF) is a critical component for online recruitment. Existing approaches face several challenges, particularly in handling low-quality job descriptions and similar candidate-job pairs, which impair model performance. To address these challenges, this paper proposes a large language model (LLM) based method with two novel techniques: (1) LLM-based data augmentation, which polishes and rewrites low-quality job descriptions by leveraging chain-of-thought (COT) prompts, and (2) category-aware Mixture of Experts (MoE) that assists in identifying similar candidate-job pairs. This MoE module incorporates category embeddings to dynamically assign weights to the experts and learns more distinguishable patterns for similar candidate-job pairs. We perform offline evaluations and online A/B tests on our recruitment platform. Our method relatively surpasses existing methods by 2.40% in AUC and 7.46% in GAUC, and boosts click-through conversion rate (CTCVR) by 19.4% in online tests, saving millions of CNY in external headhunting expenses.