An exhaust system may include an exhaust line through which exhaust gas that is formed in an engine is exhausted, a nitrogen oxide purification catalyst that is disposed on the exhaust line to reduce nitrogen oxide that is included in the exhaust gas, an injector to additionally inject fuel into the exhaust line or a cylinder, and a fuel cracking catalyst that is disposed between the injector and the nitrogen oxide purification catalyst to crack the fuel that is injected through the injector, to transform the injected fuel into a high efficiency reducing agent, and to raise the temperature of the latter part thereof through an oxidation reaction.