Severe Neonatal Jaundice (SNJ) causes long-term neurocognitive impairment, cerebral palsy, auditory neuropathy, deafness, or death. We developed a mathematical model for allo-hemodialysis as a potential blood purification method for the treatment of SNJ in term or near-term infants. With allo-hemodialysis (allo-HD), the neonate’s blood flows through hollow fibers of a miniature 0.075 m2 hemodialyzer, while the blood of a healthy adult (“buddy”) flows counter-currently through the dialysate compartment. We simulated the kinetics of unconjugated bilirubin in allo-hemodialysis with neonate blood flow rates of 12.5 and 15 mL/min (for a 2.5 kg and 3.5 kg neonate, respectively), and 30 mL/min for the buddy. Bilirubin production rates in neonate and buddy were set to 6 and 3 mg/kg/day, respectively. Buddy bilirubin conjugation rate was calculated to obtain normal steady-state bilirubin levels. Albumin levels were set to 1.1, 2.1, 3.1 g/dL for the neonate and 3.3 g/dL for the buddy. Model simulations suggest that a 6-h allo-hemodialysis session could reduce neonatal bilirubin levels by > 35% and that this modality would be particularly effective with low neonatal serum albumin levels. Due to the high bilirubin conjugation capacity of an adult’s healthy liver and the larger distribution volume, the buddy’s bilirubin level increases only transiently during allo-hemodialysis. Our modelling suggests that a single allo-hemodialysis session may lower neonatal unconjugated bilirubin levels effectively. If corroborated in ex-vivo, animal, and clinical studies, this bilirubin reduction could lower the risks associated with SNJ, especially kernicterus, and possibly avoiding the morbidity associated with exchange transfusions.