An engine output control apparatus of a vehicle, the vehicle mounting thereon an automatic transmission that transmits an engine output inputted through a torque converter to driving wheels of the vehicle, the engine output control apparatus comprising: a shift range detecting section that detects a shift range of the automatic transmission; a vehicle speed detecting section that detects a vehicle speed of the vehicle; an engine output state detecting section that detects an output state of an engine; and a controller (10, 60) that performs, on the basis of each detection information of the shift range detecting section, the vehicle speed detecting section and the engine output state detecting section, the following controls, (a) a judgment control that judges that, if the following judgment conditions (i) to (iii) are satisfied, the torque converter is in a stall state, (i) the shift range is a drive range, (ii) the vehicle speed is equal to or less than a predetermined vehicle speed, and (iii) the engine is in a high output state, (b) a cumulation control that cumulates a period of agreement of the judgment conditions if the judgment conditions are satisfied, and (c) an output suppression control that stops a part or all of fuel supply to the engine or retards the ignition timing or decrease a throttle opening, if a control start condition is satisfied by the cumulation of the agreement period, characterized in that the control start condition being set so that as the vehicle speed becomes higher, a start of the output suppression control is more delayed. a shift range detecting section that detects a shift range of the automatic transmission; a vehicle speed detecting section that detects a vehicle speed of the vehicle; an engine output state detecting section that detects an output state of an engine; and a controller (10, 60) that performs, on the basis of each detection information of the shift range detecting section, the vehicle speed detecting section and the engine output state detecting section, the following controls, (a) a judgment control that judges that, if the following judgment conditions (i) to (iii) are satisfied, the torque converter is in a stall state, (i) the shift range is a drive range, (ii) the vehicle speed is equal to or less than a predetermined vehicle speed, and (iii) the engine is in a high output state, (b) a cumulation control that cumulates a period of agreement of the judgment conditions if the judgment conditions are satisfied, and (c) an output suppression control that stops a part or all of fuel supply to the engine or retards the ignition timing or decrease a throttle opening, if a control start condition is satisfied by the cumulation of the agreement period, (a) a judgment control that judges that, if the following judgment conditions (i) to (iii) are satisfied, the torque converter is in a stall state, (i) the shift range is a drive range, (ii) the vehicle speed is equal to or less than a predetermined vehicle speed, and (iii) the engine is in a high output state, (i) the shift range is a drive range, (ii) the vehicle speed is equal to or less than a predetermined vehicle speed, and (iii) the engine is in a high output state, (b) a cumulation control that cumulates a period of agreement of the judgment conditions if the judgment conditions are satisfied, and (c) an output suppression control that stops a part or all of fuel supply to the engine or retards the ignition timing or decrease a throttle opening, if a control start condition is satisfied by the cumulation of the agreement period,