A NOx occlusion amount estimating device of a NOx-occlusion-reduction-type catalyst provided in an exhaust passage of an engine and configured to purify NOx in exhaust, the device comprising: catalyst temperature acquisition means for acquiring a catalyst temperature of the NOx-occlusion-reduction-type catalyst ; an occlusion capacity calculation means configured to calculate a NOx occlusion capacity of the catalyst on the basis of the catalyst-inlet NOx amount and the catalyst temperature; an occlusion level calculation means configured to calculate a NOx occlusion level of the catalyst on the basis of the NOx occlusion capacity calculated by the occlusion capacity calculation means ; a provisional NOx occlusion amount calculation means for calculating, as a provisional NOx occlusion amount, a NOx amount, which is to be emitted from the engine and occluded in the NOx-occlusion-reduction-type catalyst , on the basis of a catalyst-inlet NOx amount estimated from an operating state of the engine and the catalyst temperature acquired by the catalyst temperature acquisition means ; a NOx release amount calculation means for calculating a lean-time NOx release amount which is to be separated and released from the NOx-occlusion-reduction-type catalyst during a lean operation of the engine , on the basis of the catalyst temperature acquired by the catalyst temperature acquisition means during the lean operation; the NOx occlusion level acquired by the occlusion level calculation means, and a NOx release speed: an actual NOx occlusion amount calculation means for calculating an actual NOx occlusion amount occluded in the NOx-occlusion-reduction-type catalyst by subtracting the lean-time NOx release amount from the provisional NOx occlusion amount. catalyst temperature acquisition means for acquiring a catalyst temperature of the NOx-occlusion-reduction-type catalyst ; an occlusion capacity calculation means configured to calculate a NOx occlusion capacity of the catalyst on the basis of the catalyst-inlet NOx amount and the catalyst temperature; an occlusion level calculation means configured to calculate a NOx occlusion level of the catalyst on the basis of the NOx occlusion capacity calculated by the occlusion capacity calculation means ; a provisional NOx occlusion amount calculation means for calculating, as a provisional NOx occlusion amount, a NOx amount, which is to be emitted from the engine and occluded in the NOx-occlusion-reduction-type catalyst , on the basis of a catalyst-inlet NOx amount estimated from an operating state of the engine and the catalyst temperature acquired by the catalyst temperature acquisition means ; a NOx release amount calculation means for calculating a lean-time NOx release amount which is to be separated and released from the NOx-occlusion-reduction-type catalyst during a lean operation of the engine , on the basis of the catalyst temperature acquired by the catalyst temperature acquisition means during the lean operation; the NOx occlusion level acquired by the occlusion level calculation means, and a NOx release speed: an actual NOx occlusion amount calculation means for calculating an actual NOx occlusion amount occluded in the NOx-occlusion-reduction-type catalyst by subtracting the lean-time NOx release amount from the provisional NOx occlusion amount. <EOS>