An improved digital backstage calibration algorithm to calibrate high-speed pipeline Analog to Digital Converter(ADC) is introduced. This algorithm combines the slow but accurate ADC as a reference with an adaptive filter based on Least Mean Square(LMS) algorithm to rectify errors of the pipeline ADC, thereby improving the speed and accuracy of the calibration. The Verilog HDL is used to design the Register Transfer Level(RTL) circuit. At the same time, the co-simulation method of Simulink and Modelsim is adopted to verify the circuit. The verification result shows that the improved calibration algorithm has better convergence speed and accuracy compared with that of fixed-step calibration algorithm.