In the correction of various errors of TI-ADCs system, most of the current compensation algorithms are targeted for the errors in high-speed (GSPS) and medium-or-low-precision (≤16bit) TI-ADCs systems, and there are relatively few researches on nonlinearity errors. A correction algorithm for the dynamic nonlinearity mismatch errors in high-precision (24bit) TI-ADCs system was proposed. Firstly, the output data containing nonlinearity errors were extracted. Secondly, according to the truncated Volterra series error model, the dynamic nonlinearity errors coefficients were estimated with matrix transformation and LS method. Then, the nonlinearity errors were compensated by a multi-stage correction method based on error reconstruction, and the frequency spectra before and after calibration were obtained. The TI-ADCs system was simulated with single frequency, multi-frequency with equal and unequal frequency interval sinusoidal input, and the SFDR of the system after four-stage calibration was elevated from 22.91dBc, 11.12dBc and 11.14dBc to 104.45dBc, 96.74dBc and 99.25dBc, respectively. The theoretical effectiveness of the proposed method in the whole Nyquist band was verified by simulation results, which indicates a calibration effect for high-accuracy system.