Most path planning algorithms for a marine surface vehicle in the ocean environment have been developed only for a 2-D (x;y) plane without considering the vehicle heading angle. As a result, the vehicle has a difficulty in following the path correctly. In this paper, we propose a limit-cycle circle set that applies to the Theta* algorithm. The minimum turning radius of a marine surface vehicle is calculated using a limit-cycle circle set, and circles of this radius is used to generate a configuration space of an occupancy grid map. After applying Theta* to this configuration space, the limit-cycle circle set is also applied to the start and end nodes to find the appropriate path with specified heading angles. The benefit of this algorithm is its fast computation time compared to other 3-D (x;y;θ) path planning algorithms, along with the fact that it can be applied to the 3-D kinematic state of the vehicle. We simulate the proposed algorithm and compare it with 3-D A* and 3-D A* with post smoothing algorithms.