This report describes a set of neonatal electroencephalogram (EEG) recordings graded according to the severity of abnormalities in the background pattern. The dataset consists of 169 hours of multichannel EEG from 53 neonates recorded in a neonatal intensive care unit. All neonates received a diagnosis of hypoxic-ischaemic encephalopathy (HIE), the most common cause of brain injury in full term infants. For each neonate, multiple 1-hour epochs of good quality EEG were selected and then graded for background abnormalities. The grading system assesses EEG attributes such as amplitude and frequency, continuity, sleep--wake cycling, symmetry and synchrony, and abnormal waveforms. Background severity was then categorised into 4 grades: normal or mildly abnormal EEG, moderately abnormal EEG, severely abnormal EEG, and inactive EEG. The data can be used as a reference set of multi-channel EEG for neonates with HIE, for EEG training purposes, or for developing and evaluating automated grading algorithms.