A high heat-resistant catalyst support comprises an amorphous composite oxide which is constituted by:(i) an NOx storage component comprising an oxide of at least one element selected from the group consisting of alkali metals, alkaline-earth metals and rare-earth elements,(ii) alumina (Al.sub.2 O.sub.3); and(iii) at least one element selected from the group consisting of titania (TiO.sub.2), zirconia (ZrO.sub.2) and silica (SiO.sub.2).Furthermore, TiO.sub.2, ZrO.sub.2 and SiO.sub.2 are acidic, and at least one element selected from the group consisting of TiO.sub.2, ZrO.sub.2 and SiO.sub.2 is highly dispersed to form composite. So, SOx having acidity is prevented from approaching the NOx storage component, and sulfur poisoning is prevented. Moreover, bonding force of the NOx storage component to the catalyst support strengthens, and the NOx storage component is prevented from being scattered.