As logistics centers are an important hub of express transportation, their sorting efficiency has an impact on the delivery time of express packages. The coordinated sorting operations of multiple automatic guided vehicles (AGVs) can significantly improve the handling efficiency of logistics centers. This paper studies the non-conflict path planning in multi-AGV coordinated operations. The grid map is adopted to model the working environment, and a two-level path planning framework based on conflict search is proposed. In this framework, both the conflict search and constraint appending are achieved with the binary tree. When the upper level of this framework detects a conflict and adds the corresponding constraints, the lower level only needs to replan the paths of the AGVs related to the newly added constraints. The space-time A* algorithm is used to handle the path planning of a single AGV at the lower level. Furthermore, a conflict avoidance table is also introduced for avoiding the possible conflicts with existing paths of other AGVs. The simulation results demonstrate that the proposed multi-AGV path planning algorithm based on conflict search can solve various path conflicts.