Concrete pouring in the tube is one of the key procedures in the construction of concrete-filled steel tube arch bridges. Different pouring schemes greatly impact the internal force, displacement, and stability of the arch rib, and even affect the safety of the bridge structure during operation. To explore a reasonable pouring sequence of concrete in the tube, based on the principle of structural potential energy, this paper proposes a method to use the potential energy of the arch rib under the condition of the main arch bridge as a quantitative index to evaluate the quality of the pouring sequence of concrete in the tube. Based on four concrete-filled steel tube arch bridges with spans of 340 ~ 575 m, the finite element program MIDAS/civil 2019 is used to establish the simulation analysis model of the bridge, and the potential energy of the arch rib under 24 perfusion schemes is analyzed. The results show that the arch rib structure is different, and the optimal pouring sequence is also different For the half-through concrete-filled steel tube arch bridge, the optimal pouring sequence is the outer side of the top chord — the inner side of the top chord — the outer side of the bottom chord — the inner side of the bottom chord; For the deck concrete-filled steel tube arch bridge, the optimal pouring sequence is the inside of the top chord — the outside of the bottom chord — the inside of the bottom chord — the outside of the top chord. The analysis results in this study can be used for reference for the construction of the same type of bridge.