Rh and Ag are the elements neighboring Pd, which is well known as a hydrogen-storage metal. Although Rh and Ag do not possess hydrogen-storage properties, can Ag Rh alloys actually store hydrogen? Ag-Rh solid-solution alloys have not been explored in the past because they do not mix with each other at the atomic level, even in the liquid phase. We have used the chemical reduction method to obtain such Ag-Rh alloys, and XRD and STEM-EDX give clear evidence that the alloys mixed at the atomic level. From the measurements of hydrogen pressure-composition isotherms and solid-state H-2 NMR, we have revealed that Ag-Rh solid-solution alloys absorb hydrogen, and the total amount of hydrogen absorbed reached a maximum at the ratio of Ag:Rh = 50:50, where the electronic structure is expected to be similar to that of Pd.