With the development of integrated circuit process, the sizes of transistors are reducing, and the ADCs become faster with lower power consumption. On the other hand, smaller size brings more mismatch error, which will affect the accuracy, so it is necessary to introduce error calibration. In this paper, firstly, the typical error sources and traditional calibration methods of ADC were analyzed. Secondly, basic principle of neural network was given together with the most popular researches for ADC calibration based on neural network, and the advantages and disadvantages of different methods were analyzed. Finally, a system level simulation based on neural network was proposed to calibrate a 14-bit pipelined ADC. The results showed that ENOB was improved from 10 bit to 125 bit, and SFDR was improved from 80 dB to 100 dB.