Ocean environmental effects such as current, wind, water depth, and wave effects on a surface vehicle should be considered when planning the path of a marine surface vehicle, even though their complexity makes computation in a short time challenging. Moreover, the mechanical handling devices such as cranes installed on the deck floor of a surface vehicle can also severely confine a vehicle's heading angle at the goal point, especially in a docking or loading/unloading situation. This paper proposes the EEA* algorithm, a deterministic and energy-based 3-dimensional (3-D: x,y, and theta) path planning method for a marine surface vehicle on a 2-dimensional (2-D: x, y) surface plane that considers ocean environmental effects and the heading angle. The proposed path planner uses a realistic energy cost considering the loads on a vehicle due to tidal current and limited water-depth based on a given ship geometry. It also considers the vehicle's turning ability, thus generating more feasible way-points for real travel while satisfying heading angle constraints. By considering both effects in the path planning step, a more energy-efficient and maneuverable path can be found. Resultant paths and their costs are compared through various simulations in different environmental conditions with those of a classical distance-based A* algorithm, the DA* algorithm which is widely used in most applications.