The emergence of Large Language Models (LLMs) has accelerated the progress of intelligent software engineering technologies, which brings promising possibility for unit test generation. However, existing approaches on unit tests directly generated from Large Language Models (LLMs) often prove impractical due to their low coverage and insufficient mocking capabilities. This paper proposes IntUT, a novel approach that utilizes explicit test intentions (e.g. test inputs, mock behaviors, and expected results) to effectively guide the LLM to generate high-quality test cases. Our experimental results on three industry Java projects and live study demonstrate that prompting LLM with test intention can generate high-quality test cases for developers. Specifically, it achieves the improvements on branch coverage by 94% and line coverage by 49%. Eventually, we obtain developers’ feedback on using IntUT to generate cases for 3 newly Java projects with over 80% line coverage and 30% efficiency improvement on writing unit test cases.