The dataset consists of 169 multichannel EEG files of 1-hour in duration, recorded from 53 full-term newborns in the neonatal intensive care unit of the Cork University Maternity Hospital, Ireland. All 53 infants had received a diagnosis of hypoxic-ischaemic encephalopathy. The study to record the EEG was approved by the Cork Research Ethics Committee of the Cork Teaching Hospitals. Neonates were enrolled in the study after obtaining written and informed consent from a guardian or parent. The Cork Research Ethics Committee approved the publication of this fully-anonymised data set. Each 1-hour EEG was graded for severity of background abnormalities. Two experts in neonatal EEG graded each epoch independently. When grades differed between the experts, they jointly reviewed the EEG and agreed on a consensus grade. The grading system assesses EEG attributes such as amplitude and frequency, continuity, sleep--wake cycling, symmetry and synchrony, and abnormal waveforms. Four grades were used: normal or mildly abnormal (grade 1), moderately abnormal (grade 2), severely abnormal (grade 3), and inactive (grade 4). The EEG data could be used to develop automated grading algorithms or to assist in training for the review of background neonatal EEG.