The performance of analog-to-digital converters (ADCs) has reached a bottleneck due to the limitations of the manufacturing process and testing environment. Time-interleaved ADC (TIADC) technology can increase the sampling rate without changing the resolution. However, channel mismatch severely degrades the dynamic performance of the TIADC system. For the channel mismatch problem of TIADC, most of the current solutions have preconditions, such as eliminating only some kind of error or increasing the complexity of the hardware. A few methods can estimate multiple errors without changing the hardware circuit. To improve the dynamic performance of the TIADC system, on the basis of an in-depth study of the channel mismatch error of TIADC, according to the system identification theory, an identification model is designed to characterize the frequency characteristics of TIADC. Using the system observation data, the transfer function parameters of the system are recursively estimated. By constructing and verifying the identification model of the TIADC system, and then through the frequency domain correction method, a digital compensation filter is established to complete the error correction of the system. The test results of the four-channel TIADC high-speed data acquisition system show that the actual input and output characteristics of the test system are consistent with the nature of the identification model. The four channels of the TIADC system are provided by four sub-channels of two AD9653 chips, and the highest sampling rate of a single channel is 125MSPS. For sinusoidal input signals from 20 MHz to 150 MHz, the sampling system can achieve a signal-to-noise ratio (SNR) above 56.8 dB and spurious free dynamic range (SFDR) above 69.7 dB. The dynamic performance of the sampling system is nearly equivalent to that of its sub-ADC; the feasibility of the model identification method and the effectiveness of error correction are verified in simulation and experiment.