Molecular design plays a critical role in advancing fields such as drug discovery, materials science, and chemical engineering. This work introduces the Multi-Objective Large Language Model for Molecular Design (MOLLM), a novel framework that combines domain-specific knowledge with the adaptability of Large Language Models to optimize molecular properties across multiple objectives. Leveraging in-context learning and multi-objective optimization, MOLLM achieves superior efficiency, innovation, and performance, significantly surpassing state-of-the-art (SOTA) methods. Recognizing the substantial impact of initial populations on evolutionary algorithms, we categorize them into three types: best initial, worst initial, and random initial, to ensure the initial molecules are the same for each method across experiments. Our results demonstrate that MOLLM consistently outperforms SOTA models in all of our experiments. We also provide extensive ablation studies to evaluate the superiority of our components.