A background calibration algorithm based on pruning neural network was introduced, which could simultaneously calibrate multiple non-ideal factors such as capacitance mismatch, offset and gain of high-precision single-channel SAR ADC, and effectively improved the accuracy of SAR ADC. This algorithm could not only achieve the full connected neural network calibration effect, but also eliminate the weights with small contributions, which reduced the resource consumption of the calibration circuit and speeded up the neural network calibration algorithm. The simulation results showed that when the signal frequency was close to the Nyquist frequency, the 16 bit 5 MS/s SAR ADC was calibrated, and after calibration, the effective number of bits of the ADC was increased from 74 bit to 156 bit, and the spurious free dynamic range was increased from 46.8 dB to 126.2 dB.