Post-hemorrhagic hydrocephalus is a prevalent and severe neurological complication in very premature infants. Converging evidence suggests that increased ventricular size is an important and potentially modifiable risk factor for adverse neurological outcomes. MRI measures of CSF volume often rely on manual measurements to quantify ventricular size because automatic neonatal brain segmentation methods often fail in the setting of severe brain injury. In this pilot study, we proposed and validated a deep convolutional neural network method, 3D U-Net, to automatically identify the lateral ventricular system and the external cerebrospinal fluid regions. The proposed method showed superior accuracy in a preliminary cohort of 19 scans of very preterm infants compared to a conventional method.