A catalytic apparatus for exhaust purification, provided in an exhaust path of an internal-combustion engine operable with at least a theoretical air-fuel ratio and a lean air-fuel ratio, is provided with a three-way catalyst (4) having an inner layer (12a) thereof mainly containing rhodium as a noble metal to be activated in an oxygen concentration lowering atmosphere and a surface layer (12b) thereof mainly containing platinum or palladium as a noble metal to be activated in an oxygen concentration increasing atmosphere. In the catalytic apparatus, platinum or palladium in the surface layer is activated in lean operation to perform an HC purifying function effectively. If oxygen is temporarily in short supply during the change from a lean air-fuel ratio of exhaust gas over to a stoichiometric air-fuel ratio, oxygen is supplemented to purify HC by utilizing the O2 storage function of platinum or palladium as the noble metal, whereby the HC purifying rate can be prevented from temporarily suddenly lowering. The catalytic apparatus for exhaust purification can secure satisfactory HC purifying performance even in a lean area without increasing the noble metal loading of the three-way catalyst, so that it can be manufactured at low cost.