The development of the fetal cardiovascular system plays a crucial role in fetal health. The evolution of the relationship between fetal and maternal cardiac systems during fetal maturation is a characterizing feature for fetal cardiac development. This paper aims to evaluate this relationship by investigating the beat-to-beat synchronization between fetal and maternal heart rates and its variation at different stages of pregnancy. Synchronization epochs and phase locking patterns are analyzed at certain synchronization ratios (SRs) for three gestational age groups (16-26 weeks, 27-33 weeks, 34-40 weeks). Results show that the normalized synchronization epoch is significantly different for three age groups with the p-value of 6.72 10-6 and 2.89 10-4 at SR of 1-2 and 4-5 respectively. The variance of phase locking also shows significant difference for three groups with the p-value less than 10-7 at four SRs. Results also suggest that synchronization may be the force behind the increase in the maternal heart rate to maintain the fetal development and provide supplies for the fetus. Overall, the findings propose new clinical markers for evaluating the antenatal development.