This paper proposes a background calibration scheme for the pipelined-SAR ADC based on the neural network. Due to the nonlinear function fitting capability of the neural network, the linearity of the ADC is improved effectively. However, the hardware complexity of the neural network limits its application and promotion in ADC calibration. Hence, this paper also presents the optimization schemes, including the neuron-based sharing neural network and the partially binarized with fixed neural network, in terms of calibration architecture and algorithm. A 60 MS/s 14-bit pipelined-SAR ADC prototyped in 28-nm technology is utilized to verify the feasibility of the proposed calibration method. The measurement results show that the proposed calibration enhances the SFDR and SNDR from 68.3 dB and 44.6 dB to 95.4 dB and 65.4 dB at low frequency, and from 56.8 dB and 35.6 dB to 90.6 dB and 63.6 dB at Nyquist frequency. Meanwhile, the original calibrator and improved calibrator are synthesized in Synopsys Design Compiler to compare their hardware complexity. Compared with the unoptimized version, the optimized schemes can decrease the logic area and the network weights up to 76% and 52%, with negligible loss in calibration performance.