At the time of start-up, fuel supply is made excessive. When air-fuel ratio feedback control is started while the fuel is excessive, the control is put into a state of overshoot or hunting, and it takes a long time to converge to the target air-fuel ratio. In an air-fuel ratio control apparatus, a selection switch is provided at the output of an integration calculation circuit to perform air-fuel ratio feedback control, and immediately after start-up of the engine, an upper/lower limit clip value for use immediately after start-up, which is smaller than a normal one, is selected to perform the air-fuel ratio feedback control. Even if the air-fuel ratio feedback control is started immediately after the start-up in a state where the fuel is excessive, the actual air-fuel ratio does not overshoot with respect to the target air-fuel ratio and is quickly converged to the target air-fuel ratio.