To improve the performance of waveform digital readout systems based on Analog to Digital Converter (ADC) technology, this paper proposes a multi-channel mismatch error estimation calibration method. It uses two domestically produced high-speed ADCs to form a Time-interleaved A/D Conversion (TIADC) system, and the estimation of channel mismatch error (Gain, Time-skew and Offset) can be obtained by integrating particle swarm optimization (PSO) algorithm and gradient descent (GD) method. Meanwhile, it uses filter equations and Kaiser window truncation to obtain compensation calibration filter coefficient values. This compensation method can be directly implemented on the TIADC hardware platform using Field-Programmable Gate Array(FPGA) as the central processing unit. Moreover, this algorithm can achieve online reconstruction of sampling system data. The experimental results show that the algorithm can effectively compensate for channel mismatch errors, and using the behavior level simulation of Vivado development software, the spurious free dynamic range (SFDR) is increased from 32.1 dBFS to 53.1 dBFS, the SFDR is improved to 60.8 dBFS during hardware platform testing. This signal reconstruction method is also easy to implement in hardware systems and is not limited by the number of channels.