An exhaust system may include an injector mounted at an exhaust pipe or an engine and additionally injecting fuel, a diesel fuel cracking catalyst mounted at the exhaust pipe downstream of the injector and converting additionally injected fuel into a high-reactivity reducing agent through thermal cracking, a DE-NOx catalyst mounted at the exhaust pipe downstream of the diesel fuel cracking catalyst, storing the nitrogen oxide contained in the exhaust gas, and releasing the stored nitrogen oxide by the additionally injected fuel so as to reduce the nitrogen oxide through oxidation-reduction reaction with the high-reactivity reducing agent, and a control portion controlling an additional injection of fuel according to driving condition of the engine, wherein the control portion may control the injector to additionally inject the fuel according to a predetermined injection pattern in a case that driving condition of the engine satisfies an additional injection condition of the fuel and an additional injection timing condition of the fuel.