Background: Therapeutic hypothermia (TH) is a standard therapy for neonatal hypoxic-ischaemic encephalopathy. One potential additional therapy is the free radical scavenger edaravone (EV; 3-methyl-1-phenyl-2-pyrazolin-5-one). Objectives and Methods: This study aimed to compare the neuroprotective effects of edaravone plus therapeutic hypothermia (TH + EV) with those of TH alone after a hypoxic-ischaemic insult in the newborn piglet. Anaesthetized piglets were subjected to 40 min of hypoxia (3–5% inspired oxygen), and cerebral ischaemia was assessed using cerebral blood volume. Body temperature was maintained at 39.0 ± 0.5°C in the normothermia group (NT, n = 8) and at 33.5 ± 0.5°C (24 h after the insult) in the TH (n = 7) and TH + EV (3 mg/kg intravenous every 12 h for 3 days after the insult; n = 6) groups under mechanical ventilation. Results: Five days after the insult, the mean (standard deviation) neurological scores were 10.9 (5.7) in the NT group, 17.0 (0.4) in the TH group (p = 0.025 vs. NT), and 15.0 (3.9) in the TH + EV group. The histopathological score of the TH + EV group showed no significant improvement compared with that of the other groups. Conclusion: TH + EV had no additive neuroprotective effects after hypoxia-ischaemia in neurological and histopathological assessments.