In this paper, an instantaneous correlation coefficient and simplified coherent averaging method for single-channel foetal ECG (FECG) extraction is proposed. The instantaneous correlation coefficient is used to determine the position of the R peak of the measured ECG signal, and the simplified coherent averaging method is used to extract the main information of the ECG signal. The loss of the nonlinear and nonstationary characteristics by coherent averaging is recovered by threshold processing of the residual signal. The FECG signal extraction is performed in three steps. In the first step, the main information of the maternal electrocardiogram (MECG) is extracted from the abdomen electrocardiogram (AECG) signal by means of the instantaneous correlation coefficient and simplified coherent averaging method, and then the noisy FECG is obtained by subtracting the MECG obtained by simplified coherent averaging from the AECG. The second step is to extract the main information of the FECG by applying the instantaneous correlation coefficient and simplified coherent averaging method to the noisy FECG. The remaining signal is obtained by subtracting the simplified coherent averaging FECG from the noisy FECG. Thirdly, the threshold method is utilised to remove MECG residual noise and random gross value noise from the remaining signal to extract the nonlinear and nonstationary information, and the final FECG extraction is obtained by adding the nonlinear and nonstationary information to the simplified coherent averaging FECG. The validity of the proposed method is verified by experiments using synthetic data and real database data. FECG extracted by the method has the advantages of clear QRS complex wave, reasonable enhancement of P wave and T wave morphology, and no loss of nonlinear and nonstationary characteristics.