An exhaust gas control apparatus of an internal combustion engine, that is provided with a filter that is arranged in an exhaust passage of an internal combustion engine and traps particulate matter in exhaust gas, and filter regeneration controlling means for estimating an accumulated amount of particulate matter accumulated on the filter, starting filter regeneration to remove the particulate matter accumulated on the filter in response to a filter regeneration command when the estimated accumulated amount of particulate matter reaches a start-regeneration determining value, and ending the filter regeneration when the estimated accumulated amount of particulate matter decreases to an end-regeneration determining value, wherein: the filter regeneration controlling means is configured to determine that a period of time from after there is filter regeneration command and the filter regeneration starts until the filter regeneration has been completed, and which is a period of time during which the filter regeneration is not prohibited, is a period of time during which the filter is in a filter regeneration incomplete state; characterized in that, when filter regeneration is not prohibited and the filter is not in the filter regeneration incomplete state, the filter regeneration controlling means is able to select an estimation process for estimating the accumulated amount of particulate matter based on the engine operating state or an estimation process for estimating the accumulated amount of particulate matter based on a differential pressure of pressures in front and in back of the filter and in that the filter regeneration controlling means is configured to estimate the accumulated amount of particulate matter accumulated on the filter based on the engine operating state and to prevent an estimation of such accumulated amount based on a differential pressure of pressures in front and in back of the filter while the filter is in the filter regeneration incomplete state. the filter regeneration controlling means is configured to determine that a period of time from after there is filter regeneration command and the filter regeneration starts until the filter regeneration has been completed, and which is a period of time during which the filter regeneration is not prohibited, is a period of time during which the filter is in a filter regeneration incomplete state; characterized in that, when filter regeneration is not prohibited and the filter is not in the filter regeneration incomplete state, the filter regeneration controlling means is able to select an estimation process for estimating the accumulated amount of particulate matter based on the engine operating state or an estimation process for estimating the accumulated amount of particulate matter based on a differential pressure of pressures in front and in back of the filter and in that the filter regeneration controlling means is configured to estimate the accumulated amount of particulate matter accumulated on the filter based on the engine operating state and to prevent an estimation of such accumulated amount based on a differential pressure of pressures in front and in back of the filter while the filter is in the filter regeneration incomplete state.