For the complex multi-ship encounter scenarios, this article proposes a dynamic collision avoidance path planning algorithm based on the A-star algorithm and ship navigation rules, namely Dynamic Anti-collision A-star (DAA-star) algorithm. A dynamic search mechanism of the DAA-star algorithm considering time factors is designed to enable the collision avoidance for situations with known moving obstacles. A quaternion ship domain is generated based on Automatic Identification System (AIS) data, and the navigation risk cost is calculated with the combination of the quaternion ship domain and potential field. The searching constraints conforming with the Regulations for Preventing Collision at Sea (COLREGS) rules are set for the DAA-star algorithm to guarantee the safety of collision avoidance. Meanwhile, the individual ship maneuverability constraints and maneuverability differences from ship to ship are both considered in the proposed DAA-star algorithm, which can solve the path planning problem with dynamic obstacles in multi-ship encounter scenarios. The simulation results show that, compared with the traditional A-star algorithm and dynamic A-star algorithm, the DAA-star algorithm can generate more reasonable dynamic and static obstacle avoidance paths in complex navigation scenarios in the trade-off between the navigation risk and economical efficiency.