An air-fuel ratio control apparatus for an internal-combustion engine includes an air-fuel-ratio sensor, a control-input calculator, an air-fuel-ratio controller, and a gain calculator. The air-fuel-ratio sensor is disposed in an exhaust channel in the internal-combustion engine and is configured to detect an air-fuel ratio in exhaust gas. The control-input calculator is configured to calculate a control input in accordance with an output value of the air-fuel-ratio sensor. The air-fuel-ratio controller is configured to perform a feedback control using the control input such that the output value of the air-fuel-ratio sensor reaches a target value. The gain calculator is configured to calculate a gain in accordance with the output value when the output value is leaner than the target value. The gain is to be used in calculating the control input.