An exhaust purification system includes; a catalyst provided in an exhaust passage of an engine to purify an exhaust gas; a catalyst temperature estimating unit that estimates a temperature of the catalyst based on an initial temperature of the catalyst at the time of starting of the engine and a caloric value of the catalyst which changes depending on an operating state of the internal combustion engine; and an initial catalyst temperature setting unit that sets an initial temperature of the catalyst based on a catalyst temperature stored immediately before stopping the engine, a temperature of an exhaust gas flowing into the catalyst which is stored immediately before stopping the engine, a temperature of an exhaust gas flowing into the catalyst which is acquired at the time of starting the engine, and a temperature of air taken into the engine which is acquired at the time of starting the engine.