There is provided a particulate matter combustion catalyst which allows easy combustion of particulate matter collected on the particulate matter filter of a diesel vehicle, at a much lower temperature than by the prior art. The particulate matter combustion catalyst has a construction characterized by an NO oxidation catalyst wherein the catalyst component is carried on an acidic first carrier, and an NO.sub.2 decomposition catalyst wherein the catalyst component is carried on a second carrier. Preferably, the NO oxidation catalyst has a precious metal such as platinum carried on an acidic first carrier such as tungstic acid/zirconia, and the NO.sub.2 decomposition catalyst has a catalyst component selected from the transition metals carried on a second carrier such as titania, or alternatively, the NO.sub.2 decomposition catalyst has at least one metal selected from among alkali metals and alkaline earth metals and a precious metal such as platinum carried on a second carrier such as titania.