An engine control device, which is adapted for an engine provided with an NOx-absorbing material arranged in an exhaust passage for absorbing NOx in an oxygen-rich atmosphere, and releasing NOx and absorbing sulfur content when the oxygen concentration drops, includes a discriminator for judging whether the amount of sulfur absorbed by the NOx-absorbing material has reached a prescribed quantity, and a reductant concentration controller which increases the temperature of the NOx-absorbing material by decreasing a quantity related to EGR ratio for desulfurizing the NOx-absorbing material based on the result of judgment made by the discriminator. When the quantity related to the EGR ratio is decreased, the temperature of exhaust gas increases. Consequently, the temperature of the NOx-absorbing material increases and the sulfur in the NOx-absorbing material is freed and released.