To extract weak fetal ECG signals from the mixed ECG signal on the mother's abdominal wall, providing a basis for accurately estimating fetal heart rate and analyzing fetal ECG morphology. First, based on the relationship between the maternal chest ECG signal and the maternal ECG component in the abdominal signal, the temporal convolutional encoder-decoder network (TCED-Net) model is trained to fit the nonlinear transmission of the maternal ECG signal from the chest to the abdominal wall. Then, the maternal chest ECG signal is nonlinearly transformed to estimate the maternal ECG component in the abdominal mixed signal. Finally, the estimated maternal ECG component is subtracted from the abdominal mixed signal to obtain the fetal ECG component. The simulation results on the FECGSYN dataset show that the proposed approach achieves the best performance in F1 score, mean square error (MSE), and quality signal-to-noise ratio (qSNR) (98.94%, 0.18, and 8.30, respectively). On the NI-FECG dataset, although the fetal ECG component is small in energy in the mixed signal, this method can effectively suppress the maternal ECG component and thus extract a clearer and more accurate fetal ECG signal. Compared with existing algorithms, the proposed method can extract clearer fetal ECG signals, which has significant application value for effective fetal health monitoring during pregnancy.