Understanding human fetal neurodevelopment is of great clinical importance as abnormal development is linked to adverse neuropsychiatric outcomes after birth. Recent advances in functional Magnetic Resonance Imaging (fMRI) have provided new insight into development of the human brain before birth, but these studies have predominately focused on brain functional connectivity (i.e. Fisher z-score), which requires manual processing steps for feature extraction from fMRI images. Deep learning approaches (i.e., Convolutional Neural Networks) have achieved remarkable success on learning directly from image data, yet have not been applied on fetal fMRI for understanding fetal neurodevelopment. Here, we bridge this gap by applying a novel application of deep 3D CNN to fetal blood oxygen-level dependence (BOLD) resting-state fMRI data. Specifically, we test a supervised CNN framework as a data-driven approach to isolate variation in fMRI signals that relate to younger v.s. older fetal age groups. Based on the learned CNN, we further perform sensitivity analysis to identify brain regions in which changes in BOLD signal are strongly associated with fetal brain age. The findings demonstrate that deep CNNs are a promising approach for identifying spontaneous functional patterns in fetal brain activity that discriminate age groups. Further, we discovered that regions that most strongly differentiate groups are largely bilateral, share similar distribution in older and younger age groups, and are areas of heightened metabolic activity in early human development.