Fetal heart rate monitoring using the abdominal electrocardiograph (ECG) is an important topic for the diagnosis of heart defects. Many studies on fetal heart rate detection have been presented, however, their accuracy is still unsatisfactory. That is because the fetal ECG waveform is contaminated by maternal ECG interference, muscle contractions, and motion artifacts. One of the conventional methods is to detect the R-peaks from the integrated power of the frequency corresponding to the fetal heartbeats. However, the detection accuracy of the R-peaks is not enough. In this paper, we propose a method to generate the candidates of R-peaks using the first derivative of the signal and to pick up the estimated heartbeats by a multiple weighting function. The proposed multiple weighting function is designed by the Gaussian distribution, of which parameters are set from a grid search with the goal of minimizing the standard deviation of RR intervals (neighboring R-peaks intervals). The validation for the proposed framework has been evaluated on real-world data, which got the better accuracy than the conventional method that detects R-peaks from the integrated power and uses the weighting function produced by a fixed parameter of Gaussian distribution . The averaged absolute error (AAE) which compares the estimated fetal heart rate and the reference fetal heart rate has been decreased by 17.528 bpm.