An exhaust gas purification apparatus for an internal combustion engine includes a filter supporting the catalyst with an oxygen storage capacity, an air fuel ratio sensor to detect an air fuel ratio of exhaust gas at the downstream side of the filter, and a controller configured to change an air fuel ratio of exhaust gas flowing into the filter, to estimate an amount of particulate matter deposited in an interior of a partition wall of the filter, estimate a maximum storable oxygen amount of the catalyst from a change of the air fuel ratio of exhaust gas obtained by the air fuel ratio sensor at the time when the air fuel ratio of exhaust gas is changed by the controller, and correct the maximum storable oxygen amount of the catalyst based on the amount of particulate matter deposited in the interior of the partition wall of the filter.