Large language models (LLMs) are widely applied in various natural language processing tasks such as question answering and machine translation. However, due to the lack of labeled data and the difficulty of manual annotation for biochemical properties, the performance for molecule generation tasks is still limited, especially for tasks involving multi-properties constraints. In this work, we present a two-step framework PEIT (Property Enhanced Instruction Tuning) to improve LLMs for molecular-related tasks. In the first step, we use textual descriptions, SMILES, and biochemical properties as multimodal inputs to pre-train a model called PEIT-GEN, by aligning multi-modal representations to synthesize instruction data. In the second step, we fine-tune existing open-source LLMs with the synthesized data, the resulting PEIT-LLM can handle molecule captioning, text-based molecule generation, molecular property prediction, and our newly proposed multi-constraint molecule generation tasks. Experimental results show that our pre-trained PEIT-GEN outperforms MolT5, BioT5, MolCA and Text+Chem-T5 in molecule captioning, demonstrating modalities align well between textual descriptions, structures, and biochemical properties. Furthermore, PEIT-LLM shows promising improvements in multi-task molecule generation, demonstrating the effectiveness of the PEIT framework for various molecular tasks. The code and appendix are available at https://github.com/chenlong164/PEIT.