Software testing plays a crucial role in software engineering, ensuring the reliability and correctness of evolving systems.Well-maintained test suites are essential for ensuring software quality.However, in modern development cycles that emphasize rapid feature iteration, the co-evolution of test suites often lags behind, leading to more appearance of obsolete tests.To this end, automated approaches for updating obsolete test code have been proposed, and recent approaches have achieved the state-of-the-art performance with the support of large language models (LLMs). This paper presents CommitUp, a new approach that leverages LLMs to effectively automate method-level obsolete test code updates.CommitUp mimics how humans solve the problem, first comprehending the code modifications, searching for similar examples to imitate, and finally performing the update.We evaluate CommitUp on a curated dataset from real-world Java projects. The results demonstrate the superior performance of CommitUp, achieving 96.4%, 94.4%, 93.1% success rates for generating compilable, runtime failure-free, and full coverage updates, respectively. We believe our study can provide new insight into LLM-based test code update. The dataset and code are available at https://anonymous.4open.science/r/CommitUp.