To study the mechanical properties and time-varying characteristics of initial damaged composite beams under concrete shrinkage and creep, a novel solid slip finite element model of steel-concrete composite beams was constructed by using solid element to simulate shear studs. And the model was validated by both experiments and theoretical calculation. Considering different damage conditions, the degradation law of mechanical properties of composite beams with initial damages was revealed from the aspects of bearing capacity, stiffness degradation and interface slip distribution. The coupling effects of asymmetric initial damage and concrete shrinkage and creep on mechanical properties such as the vertical deformation, interface slip, stress redistribution and shear force were investigated. The deformation and section stress growth regulations were disclosed, as well as the damage mechanism of shear studs and its nearby concrete. The results show that the local asymmetric damage induced the asymmetric distribution of interface slips. The interface slip value and stiffness change are 1.37 and 1.25 times higher than that of symmetric condition under the same damage degree. Under the multi-coupling effect of initial stud damage and concrete shrinkage and creep, the maximum interface slip and shear force transferres to the nearby stud, accompanied by the stress decrease in concrete wings and stress increase in steel beam, the vertical deformation and section stress growth of the composite beam can be expressed by the constructed logarithmic model.