An exhaust purification apparatus comprising: a urea water supplier that is configured to supply urea water into an exhaust passage in which exhaust discharged from an internal-combustion engine flows; a nitrogen oxide trapping catalyst that is disposed on an exhaust upstream side of the urea water supplier, the nitrogen oxide trapping catalyst that is configured to occlude nitrogen oxide contained in the exhaust under an oxidizing atmosphere, and is configured to reduce the nitrogen oxide under a reducing atmosphere; a selective reduction catalyst that is disposed on an exhaust downstream side of the urea water supplier, the selective reduction catalyst that is configured to reduce the nitrogen oxide contained in the exhaust by using the urea water supplied from the urea water supplier as a reducing agent; and a controller that is configured to control an amount of supply of the urea water supplied from the urea water supplier, and that has a normal mode, a decrease mode in which the amount of supply of the urea water supplied from the urea water supplier is suppressed in comparison to the normal mode, and a decrease return mode in which the controller is configured to control the urea water supplier so as to increase, in comparison to the decrease mode, the amount of supply of the urea water supplied from the urea water supplier, wherein the exhaust purification apparatus further comprises a urea catalyst temperature detector that is configured to detect a temperature of the selective reduction catalyst and a trapping catalyst temperature detector that is configured to detect a temperature of the nitrogen oxide trapping catalyst, wherein the controller is configured to set the decrease mode when the temperature of the selective reduction catalyst detected by the urea catalyst temperature detector is equal to or higher than a first predetermined temperature, and the controller is configured to set the decrease return mode when the temperature of the nitrogen oxide trapping catalyst detected by the trapping catalyst temperature detector is equal to or higher than a second predetermined temperature, which is higher than the first predetermined temperature. a urea water supplier that is configured to supply urea water into an exhaust passage in which exhaust discharged from an internal-combustion engine flows; a nitrogen oxide trapping catalyst that is disposed on an exhaust upstream side of the urea water supplier, the nitrogen oxide trapping catalyst that is configured to occlude nitrogen oxide contained in the exhaust under an oxidizing atmosphere, and is configured to reduce the nitrogen oxide under a reducing atmosphere; a selective reduction catalyst that is disposed on an exhaust downstream side of the urea water supplier, the selective reduction catalyst that is configured to reduce the nitrogen oxide contained in the exhaust by using the urea water supplied from the urea water supplier as a reducing agent; and a controller that is configured to control an amount of supply of the urea water supplied from the urea water supplier, and that has a normal mode, a decrease mode in which the amount of supply of the urea water supplied from the urea water supplier is suppressed in comparison to the normal mode, and a decrease return mode in which the controller is configured to control the urea water supplier so as to increase, in comparison to the decrease mode, the amount of supply of the urea water supplied from the urea water supplier, wherein the exhaust purification apparatus further comprises a urea catalyst temperature detector that is configured to detect a temperature of the selective reduction catalyst and a trapping catalyst temperature detector that is configured to detect a temperature of the nitrogen oxide trapping catalyst, wherein the controller is configured to set the decrease mode when the temperature of the selective reduction catalyst detected by the urea catalyst temperature detector is equal to or higher than a first predetermined temperature, and the controller is configured to set the decrease return mode when the temperature of the nitrogen oxide trapping catalyst detected by the trapping catalyst temperature detector is equal to or higher than a second predetermined temperature, which is higher than the first predetermined temperature.