Finetuning a Large Language Model (LLM) is crucial for generating results towards specific objectives. This research delves into the realm of drug optimization and introduce a novel reinforcement learning algorithm to finetune a drug optimization LLM-based generative model, enhancing the original drug across target objectives, while retains the beneficial chemical properties of the original drug. This work is comprised of two primary components: (1) DrugImprover: A framework tailored for improving robustness and efficiency in drug optimization. It includes a LLM designed for drug optimization and a novel Structured Policy Optimization (SPO) algorithm, which is theoretically grounded. This algorithm offers a unique perspective for fine-tuning the LLM-based generative model by aligning the improvement of the generated molecule with the input molecule under desired objectives. (2) A dataset of 1 million compounds, each with OEDOCK docking scores on 5 human proteins associated with cancer cells and 24 binding sites from SARS-CoV-2 virus. We conduct a comprehensive evaluation of SPO and demonstrate its effectiveness in improving the original drug across target properties. Our code and dataset will be publicly available at: https://github.com/xuefeng-cs/DrugImproverGPT.