To provide a catalyst for purifying exhaust gas in which low- temperature activity is enhanced during the period from the early stage to full operation after durableness and the purification rate of HC, CO, NOx is enhanced even in such the reduction atmosphere that the concentration of oxygen is insufficient while keeping a theoretical air-fuel ratio as a center.

The catalytic material for purifying exhaust gas contains alumina-based compound oxide incorporating nickel and cerium. Alumina-based compound oxide is shown in the following general formula. [X]a[Y]bAlcOd (in formula, X is cerium element, Y is nickel element and (a), (b), (c) and (d) show atomic ratio of each element. At time when (c) is 2.0, (a) is 0.01-0.10, (b) is 0.1-0.7, (d) is number of oxygen atoms necessary for satisfying valency of the above-mentioned each component.) The catalyst for purifying exhaust gas is constituted by carrying noble metal on the catalytic material for purifying exhaust gas.