In comparison with the short-term behavior of bridges in the early stages of their service life, predicting the long-term behavior of the concrete due to their shrinkage and creep effects is a more complex and difficult task. Curved steel-concrete composite box bridge girders have been widely used in urban highway interchanges and ramp bridges due to their lightness in weight, long spanning capacity, and high torsional stiffness. Presently, there are a few experimental studies on the long-term behavior of steel-concrete composite beams, but none of them focus on curved composite box beams. This paper reports the long-term test results of 5 scaled curved composite box beams, including 4 simply supported beams and 1 continuous beam. The span length of the 4 simply supported beams is 6.2 m and the span length of the 2-span continuous beam is 6.8 m. The beams are tested under sustained uniformly distributed loading for 222 days. In the test, the vertical deflection, interfacial slip between the concrete and the steel beam, rotational angle, and normal strain of the concrete slabs, rebars, and steel beams are measured. In addition, a concrete prism specimen is tested under uniaxial compression to measure the shrinkage and creep effects under the same environmental conditions as the beams. The research shows that shrinkage and creep of the concrete have significant effects on the long-term mechanical performance of composite beams. This experimental study contributes to the literature on the long-term behavior of composite beams and provides data for subsequent studies on the development of theoretical and numerical models of curved composite box beams.