In order to analyze the long-term creep law and its influencing factors of steel box - concrete composite curved beam bridge, the possible prevention and control measures are put forward. The finite element analysis model of steel box - concrete curved composite beam bridge is established by using ABAQUS finite element software. The simulation methods of support friction and slippage, long-term fine temperature field and vehicle centrifugal force are proposed respectively. The variation laws of tangential and radial displacement of the supports of curved beam bridge for two consecutive years under the combined action of these factors are analyzed. The theoretical basis is provided for the creep prevention of steel box - concrete composite curved girder bridge.