The performance of an analog-to-digital converter (ADC) determines the quality of the entire acquisition system. With the increase in sampling rate and bandwidth, nonlinear errors pose a greater threat than linear errors. This paper proposes an adaptive parameter estimation method based on sine wave fitting combined with the normalized least mean squares (NLMS) algorithm to calibrate frequency-dependent nonlinear errors in ADCs through digital post-calibration. The method first performs sine wave fitting on the single-tone signal collected by the ADC and then reconstructs the nonlinear error signal based on the fitting output and the Volterra series model. The NLMS algorithm is employed to adaptively estimate the parameters related to the Volterra series model. When the parameters converge, the deviation between the corrected ADC sampling sequence and the fitting output approaches zero. This method requires only a small number of sampling points to converge and involves no complex computations, resulting in low resource overhead. Simulations and experiments have validated the effectiveness of the proposed algorithm. In the simulation, the second harmonic and third harmonic components are attenuated by more than 20 and 15 dB, respectively. Furthermore, the overall nonlinear spurious components of the wideband multi-tone signal are reduced by more than 15 dB after calibration. The proposed method was validated on a hardware platform with a sampling rate of 20 GSPS and demonstrated effective calibration performance, resulting in an overall improvement in the spurious-free dynamic range (SFDR) of approximately 10 dB.