The invention belongs to the technical field of analog-digital converters, and particularly relates to a capacitive nonlinear calibration circuit of a bit-by-bit approximation analog-digital converter and a method. The circuit structurally comprises a digital-analog converter, a clock control circuit, a calibration logic control circuit, an error measurement and storage circuit, a summator logic circuit, a comparator circuit and a bit-by-bit approximation analog-digital converter logic circuit. The method comprises the steps that the calibration logic control circuit is switched on, the analog-digital converter starts to carry out error measurement, and the error measurement and storage circuit calculates and stores the error factors of capacitors on all bits respectively; after the error factors are all stored, the calibration logic control circuit is switched off, and the analog-digital converter adds output codes and the error factors through the summator to obtain the final calibration output code. The capacitive nonlinear calibration circuit and the method are suitable for the high-precision low-power-consumption bit-by-bit approximation analog-digital converter, and mainly have the advantage that under the condition of not adding extra analog circuits, nonlinear errors caused by stray capacitors and capacitor array mistaching in a calibration capacitor array and hardware and power consumption cost are low.