This invention relates to regeneration of a filter (41) which traps particulate matter contained in the exhaust gas of a diesel engine (1) for a vehicle. A programmable controller (31) performs filter regeneration appropriately in accordance with the running pattern of the vehicle by calculating a first parameter indicating the frequency with which the diesel engine (1) performs an idling operation over a predetermined time period up to the present (S7), calculating a second parameter indicating the temperature environment of the filter (41) over a predetermined time period up to the present (S3), and determining whether or not the filter (41) can be regenerated completely on the basis of the first parameter and second parameter (S13).