The problem of path planning for UUV in time-varying ocean flows is considered. A method of path planning with biased extension is proposed to guarantee that the path is feasible and optimal. Considering the anisotropy of ocean flows and the motion constraint of UUV, a simplified space is obtained after the sub-nodes are expanded in special orientation. An integrated cost function is proposed to fulfill the requirement of different missions, including the energy expenditure, travel time, and obstacle avoidance. In the end, A* based algorithm is applied for path search. Simulation results illustrate the proposed approach is simple and fast, and the path posed is feasible for trail.