Rutting is one of the common distresses observed in asphalt pavement, influenced by temperature and load conditions. To clarify the permanent deformation behavior of steel-concrete composite beam (SCCB) bridge deck pavement under temperature-load coupling effect and provide references for the distress cause analysis, five typical SCCB bridge deck pavements were selected. The temperature distribution and the temperature stress of the pavement structures were analyzed by numerical simulation under periodic temperature variations. In addition, considering the daily variation in traffic volume, the permanent deformation of the five pavement structures were calculated under temperature-load coupling effect. Finally, the influence of heavy load on the development of rutting distress was also investigated. The results show that the temperature field and temperature stresses within the SCCB bridge deck pavement exhibit periodic variations under periodic temperature variations. Additionally, after 500,000 times of standard axle load application, “EA + SMA” exhibits the smallest permanent deformation and the best resistance to rutting distress under temperature-load coupling effect. Finally, heavy load conditions have a great influence on the permanent deformation of SCCB bridge deck pavement. In areas with severe rutting distresses, it is recommended to use “EA + SMA” pavement structure in SCCB bridge.