Offering rich contexts to Large Language Models (LLMs) has shown to boost the performance in various tasks, but the resulting longer prompt would increase the computational cost and might exceed the input limit of LLMs. Recently, some prompt compression methods have been suggested to shorten the length of prompts by using language models to generate shorter prompts or by developing computational models to select important parts of original prompt. The generative compression methods would suffer from issues like hallucination, while the selective compression methods have not involved linguistic rules and overlook the global structure of prompt. To this end, we propose a novel selective compression method called PartPrompt. It first obtains a parse tree for each sentence based on linguistic rules, and calculates local information entropy for each node in a parse tree. These local parse trees are then organized into a global tree according to the hierarchical structure such as the dependency of sentences, paragraphs, and sections. After that, the root-ward propagation and leaf-ward propagation are proposed to adjust node values over the global tree. Finally, a recursive algorithm is developed to prune the global tree based on the adjusted node values. The experiments show that PartPrompt receives the state-of-the-art performance across various datasets, metrics, compression ratios, and target LLMs for inference. The in-depth ablation studies confirm the effectiveness of designs in PartPrompt, and other additional experiments also demonstrate its superiority in terms of the coherence of compressed prompts and in the extreme long prompt scenario.