An exhaust purification system comprising: a catalyst that is provided in an exhaust passage of an internal combustion engine to purify an exhaust gas; a catalyst temperature estimating unit (80, 87, 88) configured to estimate a temperature of the catalyst based on an initial temperature of the catalyst at the time of starting of the internal combustion engine and a caloric value of the catalyst which changes depending on an operating state of the internal combustion engine; a pre-stop catalyst temperature storing unit (102A, 102B) configured to store the temperature of the catalyst estimated by the catalyst temperature estimating unit (80, 87, 88) immediately before stopping the internal combustion engine, as a pre-stop catalyst temperature; a first exhaust temperature storing unit configured to store a temperature of an exhaust gas flowing into the catalyst immediately before stopping the internal combustion engine, as a first exhaust temperature; a second exhaust temperature acquiring unit configured to aquire a temperature of an exhaust gas flowing into the catalyst at the time of starting the internal combustion engine, as a second exhaust temperature; an intake air temperature acquiring unit configured to aquire a temperature of air taken into the internal combustion engine at the time of starting the internal combustion engine, as an intake air temperature; and an initial catalyst temperature setting unit (103A, 103B, 104A, 104B, 105A, 105B, 106A, 106B) configured to set an initial temperature of the catalyst based on the pre-stop catalyst temperature, the first exhaust temperature, the second exhaust temperature, and the intake air temperature. a catalyst that is provided in an exhaust passage of an internal combustion engine to purify an exhaust gas; a catalyst temperature estimating unit (80, 87, 88) configured to estimate a temperature of the catalyst based on an initial temperature of the catalyst at the time of starting of the internal combustion engine and a caloric value of the catalyst which changes depending on an operating state of the internal combustion engine; a pre-stop catalyst temperature storing unit (102A, 102B) configured to store the temperature of the catalyst estimated by the catalyst temperature estimating unit (80, 87, 88) immediately before stopping the internal combustion engine, as a pre-stop catalyst temperature; a first exhaust temperature storing unit configured to store a temperature of an exhaust gas flowing into the catalyst immediately before stopping the internal combustion engine, as a first exhaust temperature; a second exhaust temperature acquiring unit configured to aquire a temperature of an exhaust gas flowing into the catalyst at the time of starting the internal combustion engine, as a second exhaust temperature; an intake air temperature acquiring unit configured to aquire a temperature of air taken into the internal combustion engine at the time of starting the internal combustion engine, as an intake air temperature; and an initial catalyst temperature setting unit (103A, 103B, 104A, 104B, 105A, 105B, 106A, 106B) configured to set an initial temperature of the catalyst based on the pre-stop catalyst temperature, the first exhaust temperature, the second exhaust temperature, and the intake air temperature.