In this study we present a non-invasive method which enables the investigation of the Fetal Heart Rate (FHR) fluctuations. The objective was to design a quantitative measurement to assess the fetal Autonomic Nervous System (ANS) and to investigate its development as a function of the gestational age. Our Medical Physics group has developed a complex algorithm for on-line beat-to-beat detection of the Fetal ECG (FECG), extracted from the maternal abdominal ECG signal. We used our previously acquired FECG data which includes non-invasive recordings of 200 maternal abdominal ECG signals. From these, we chose 35 cases of healthy pregnancies which we divided into three groups according to gestational age: Group 1 - 23±2 weeks, Group 2 - 32±1 weeks, and Group 3 - 39±1 weeks. The FHR Variability (FHRV) was analyzed by a time-frequency decomposition based on a Continuous Wavelet Transform (CWT). We have shown that independently of the gestational age most of the FHR power is concentrated in the Very Low Frequency (VLF) range (0.02-0.08Hz) and in the Low Frequency (LF) range (0.08-0.2Hz). In addition, there is power in the High Frequency (HF) range that correlates with the frequency range of fetal respiratory motion (0.4-1.7Hz). In the intermediate frequency range (0.2-0.4Hz), the power is significantly smaller. The changes in the average power spectrum in relation to gestation time were carefully and quantitatively examined. The results imply that there is a neural organization during the last trimester of the pregnancy, and the sympatho-vagal balance is reduced with the gestational age.