A diesel engine is provided with an exhaust fuel addition valve capable of adding fuel from an exhaust passage on an upstream side of an exhaust post-treatment device. An ECU, which is a control unit of the diesel engine, has a function to estimate biofuel concentration in the fuel and a function to obtain an exhaust temperature in the exhaust passage. The ECU sets a minimum operating exhaust temperature, which is a lower limit value of the exhaust temperature to permit operation of the exhaust fuel addition valve, according to the estimated biofuel concentration. The fuel added from the exhaust fuel addition valve is sufficiently vaporized in exhaust gas having temperature not lower than a minimum operation permission exhaust temperature set according to the biofuel concentration and is allowed to flow to the exhaust post-treatment device.