In this investigation, the uniaxial short-term creep tests with multi-step loading were conducted on the sandstone-coal composite samples, and the characteristics of creep strength, creep deformation, acoustic emission (AE), and creep failure of composite samples were studied, respectively. The creep strength of the composite sample decreased with the stress-level duration, which was mainly determined by the coal and influenced by the interactions with the sandstone. The creep deformation and damage of sandstone weakened the deformation and damage accumulation within the coal, resulting in the larger strength for the composite sample compared with the pure coal sample. The axial creep strain of composite sample generally increased with the stress-level or the stress-level duration under same conditions. The AE characteristics of composite sample were related to the creep strain rate, the stress level, the stress level duration, and the local failure or fracture during creep loading. The micro or macro failure and fracture within the composite sample caused the rise in the axial creep strains and the frequency and intensity of AE signals, especially the macro failure and fracture. The creep failures of composite samples mainly occurred within the coal with the splitting ejection failure accompanied by the local shear failure, and no obvious failures were found within the sandstone. The coal in the composite sample became more broken with the stress-level duration.