First-principles calculations of the core-level binding energy shifts (CLS) for 3d inner-core electrons of Ag and Pd in fcc Ag-Pd alloy were carried out within the complete screening picture, which includes both initial and final state effects. These alloys show remarkable CLS that have the same sign for both alloy components, in contradiction to what would be expected from the potential model for core electron energies. We show that the main contribution to the core-level shift is due to the intra-atomic charge redistribution, which is related to the hybridization between the valence electron states of the alloy components. There is also a large contribution to the CLS from the core-hole relaxation energy.