When it is determined that fuel in use is low-cetane fuel or a present location point is at a high altitude, a map of rich combustion, exhaust gas fuel addition or a post-injection is rewritten on the occasion of reduction of NOx to inhibit a misfire. Also, deterioration of fuel consumption due to regeneration of a diesel particulate filter is inhibited by suppressing excessive discharge of smoke due to the rich combustion. Thus, an exhaust purification device of an internal combustion engine capable of achieving both of inhibition of the deterioration in the fuel consumption due to the regeneration of the diesel particulate filter and inhibition of torque shock accompanying the misfire during the rich combustion for the NOx reduction is provided.