For multiple Automated Guided Vehicles (AGVs) system, it is required to realize just-in-time delivery to minimize the earliness and tardiness of the specified delivery time not only to minimize the total traveling time. In this paper, we propose a heuristic algorithm for just-in-time and conflict-free routing problem of AGVs. The proposed method can derive a near-optimal task assignment and routing and scheduling of multiple AGVs to improve both the JIT performance and the total completion time. In the proposed method, a strategy to avoid collisions ensuring feasibility is proposed. The effectiveness of the proposed method is demonstrated by comparing the performance with CPLEX from computational results. The results show that the proposed method can obtain a better solution which is close to an optimal solution with a significantly shorter computational time than that derived from CPLEX.