Tree-structured large language model (LLM) programs are increasingly employed in many applications. Existing LLM serving systems use a radix tree to organize the global key-value (KV) cache, facilitating cache reuse across different queries and thus reducing unnecessary memory use. Despite this, these systems still rely on conventional computation patterns for attention operations, resulting in redundant memory loads and GPU tensor core underutilization. To address these limitations, we present FastTree, which introduces GPU kernels tailored for efficiently processing queries that share contexts through the radix tree. To effectively employ the FastTree kernels, a significant challenge arises in finding optimal context-queries pairs with a given KV cache tree, as the varying shared prefixes between queries create a giant decision space. To tackle this, we propose tree structure-adaptive runtime optimization within FastTree, applying a greedy heuristic to partition the tree to minimize overhead and splitting lengthy contexts to mitigate the tail effect. FastTree is built upon SGLang, and extensive experiments demonstrate that it improves the throughput of SGLang by up to 1.9×.