Ship path planning is one of the key technologies for ship automation. Establishing a cooperative collision avoidance (CA) path for multi-ship encounters is of great value to maritime intelligent transportation. This study aims to solve the problem of multi-ship collaborative collision avoidance based on the algorithm of Conflict Search (CS) and Space-Time Hybrid A-star (STHA). First, a static CA path is searched for each ship by using the space-time Hybrid A-star algorithm, and the conflict risk area is determined according to the ship safety distance constraint and fuzzy Collision Risk Index (CRI). Secondly, the space-time conflict constraint is introduced into the multi-ship cooperative CA scheme, and the binary tree is used to search for an optimal navigation path with no conflict and low cost. In addition, the optimal path is smoothed by using cubic interpolation to make the path consistent with actual navigation practice and ship maneuvering characteristics. Finally, considering the constraints of the International Regulations for Preventing Collisions at Sea (COLREGs), the typical two-ship and multi-ship encounter scenarios are designed and simulated to verify the effectiveness of the proposed method. Furthermore, a comparative analysis of actual encounters and encounters based on CS-STHA is also carried out. The results indicate that the proposed algorithm in the study can obtain an optimal CA path effectively and provide a reference of CA decision-making for autonomous ships.