The present invention provides a catalyst for purifying a combustion exhaust gas and a method for purifying a combustion exhaust gas, capable of efficiently removing a nitrogen oxide in an exhaust gas in a relatively low temperature range discharged from an internal combustion engine, such as a marine diesel engine, with a smaller amount of the reducing agent than the ordinary techniques. The catalyst for purifying a combustion exhaust gas is a catalyst used in a purification method of a combustion exhaust gas of removing a nitrogen oxide in a combustion exhaust gas by making the catalyst into contact with the combustion exhaust gas having an alcohol added thereto as a reducing agent, the catalyst containing a catalyst support containing zeolite, having supported thereon at least one metal selected from the group consisting of Ag (silver), Bi (bismuth), and Pb (lead).