Underwater vehicle is essential for many tasks such as underwater exploration, equipment deployment and covert reconnaissance. Many underwater missions must be carried out with stealth to avoid being detected by enemy sonars, and safety and security are required in such high-risk situations. In this paper, a covert path planning algorithm for underwater vehicle is proposed based on the sonar detection probability analysis. First the sonar performance prediction model is constructed with sonar parameters, marine environment and underwater vehicle acoustic properties. Afterwards an improved ant colony algorithm is established by minimizing the cumulative detection probability. The evaluation indicate that the optimal covert path obtained for underwater vehicle is effective for reducing the cumulative detection probability.