Abstract: Offset error, gain error and time error greatly degrade the signal-to-noise ratio (SNR) and effective number of bits (ENOB) in time-interleaved analog to digital converter (ADC) systems. This paper discusses mathematical statistics and spectrum analysis calibration method for time-interleaved ADC systems. Mathematical statistics is used for offset error, through mathematical statistics of the sampled data of each sub ADC, the estimation of the offset error can be obtained, and the calibration can be carried out. Meanwhile, a second time calibration is applied to improve the calibration accuracy, the spectrum analysis is used for gain error and time error. The gain error and time error can be estimated by the magnitude and phase of the specific frequency point, so the calibration can be achieved. The comparison of the signal spectrums before and after calibration proves the effectiveness of the calibration algorithm. The algorithm is simple and easy to implement. The experiment result shows that the SNR can reach to 41.019 4 dB, and ENOB to 6.52 bit. Moreover, the results is equal or better than the sine fitting algorithm.