A catalyst with a supported platinum-group metal, the catalyst comprising: an organic porous anion exchanger which is a continuous macroporous structure having cellular macropores overlapping each other, the overlapping parts in a water-wet state forming openings having an average diameter of 30-300 [mu]m, and has a total pore volume of 0.5-5 mL/g and a water-wet-state anion-exchange capacity of 0.4-1.0 mg-eq/mL, and in which anion-exchange groups are evenly distributed in the organic porous anion exchanger and, in an SEM image of a cut section of the continuous macroporous structure (dry state), the area of skeletal parts appearing in the section is 25-50% of the image region; and platinum-group metal nanoparticles having an average particle diameter of 1-100 nm and deposited on the anion exchanger in an amount of 0.004-20 wt.% in terms of dry-state content. This catalyst is a high-performance catalyst which renders the decomposition and removal of hydrogen peroxide or the removal of dissolved oxygen possible even when water is passed at a high SV exceeding 2,000 h-1 and when the catalyst is packed in a reduced thickness.