Non-invasive measurement of uterine activity using electrohysterogram (EHG) surface electrodes has been attempted to monitor uterine contraction. This study aimed to computationally compare the performance of acquiring EHG signals using monopolar electrode and three types of Laplacian concentric ring electrodes (bipolar, quasi-bipolar and tri-polar). With the implementation of dipole band model and abdomen model, the performances of four electrodes in terms of the local sensitivity were quantified by potential attenuation. Furthermore, the effects of fat and muscle thickness on potential attenuation were evaluated using the bipolar and tri-polar electrodes with different radius. The results showed that all the four types of electrodes detected the simulated EHG signals with consistency. That the bipolar and tri-polar electrodes had greater attenuations than the others, and the shorter distance between the origin and location of dipole band at 20 dB attenuation, indicating that they had relatively better local sensitivity. In addition, ANOVA analysis showed that, for all the electrodes with different outer ring radius, the effects of fat and muscle on potential attenuation were significant (all p < 0.01). It is therefore concluded that the bipolar and tri-polar electrodes had higher local sensitivity than the others, indicating that they can be applied to detect EHG effectively.