In an exhaust purifying apparatus, a fuel adding valve (31) supplies unburned fuel to an exhaust passage (14) of a diesel engine (10) so that particulate matter collected in a catalytic converter (33) is burned and removed. The supply of unburned fuel from the fuel adding valve (31) is executed even after an electronic control unit (41) determines that particulate matter in the catalytic converter (33) has been burned and removed. This reduces the amount of particulate matter remaining unburned in the catalytic converter (33).