To regenerate a diesel particulate filter (10) which traps particulate matter contained in the exhaust gas of a diesel engine (20), a controller (16) raises the temperature of the exhaust gas through fuel injection control of a fuel injector (23), and thus burns the particulate matter trapped in the filter (10). The controller (16) cumulatively calculates the time during which the temperature of the filter (10) exceeds a target temperature as an effective regeneration time. By estimating the amount of particulate matter remaining in the filter (10) on the basis of the effective regeneration time, the controller (16) estimates the amount of remaining particulate matter with a high degree of precision and without consuming energy, whereupon regeneration of the filter (10) through fuel injection control ends.