The autonomous mobility-on-demand (AMoD) system provides an alternative solution for sustainable and economical transportation system. Meanwhile, battery swapping could become a promising approach to sustain the efficient operation of EV fleet. This article proposes a combined operation scheme for battery swapping station (BSS) and AMoD system. To maximizing the profit of AMoD system, an expanded network flow model is employed to determine swapping scheduling and vehicle rebalancing for EV fleet in AMoD system. The interaction between the shared mobility-on-demand system and BSS is modeled by the swapping demand and swapping price. Specifically, swapping demand is determined in the AMoD system and introduced as known parameters in the BSS problem. Fleet management operation in AMoD system will be influenced by swapping price provided by BSS. The BSS management problem is formulated as a mixed-integer linear programming model, which optimizes refueling decisions for depleted batteries. Simulation experiments based on real-world data from New York City are provided. The results demonstrate the effectiveness of this proposed integrated operation model.