Fetal electrocardiogram (ECG) signals provide important clinical information for early diagnosis and intervention of fetal abnormalities. In this paper, we propose a new method for fetal ECG signal extraction and analysis. Firstly, an improved fast independent component analysis method and singular value decomposition algorithm are combined to extract high-quality fetal ECG signals and solve the waveform missing problem. Secondly, a novel convolutional neural network model is applied to identify the QRS complex waves of fetal ECG signals and effectively solve the waveform overlap problem. Finally, high quality extraction of fetal ECG signals and intelligent recognition of fetal QRS complex waves are achieved. The method proposed in this paper was validated with the data from the PhysioNet computing in cardiology challenge 2013 database of the Complex Physiological Signals Research Resource Network. The results show that the average sensitivity and positive prediction values of the extraction algorithm are 98.21% and 99.52%, respectively, and the average sensitivity and positive prediction values of the QRS complex waves recognition algorithm are 94.14% and 95.80%, respectively, which are better than those of other research results. In conclusion, the algorithm and model proposed in this paper have some practical significance and may provide a theoretical basis for clinical medical decision making in the future.