We performed general anesthesia for a lip repair and palatoplasty in a patient with left ventricular hypoplasia following a Glenn procedure. Preoperative examination revealed hemorrhagic diathesis, hypoxemia, and secondary polycythemia. After completion of the palatoplasty, hypoxemia and intraoral bleeding were observed, and reintubation was required. The bleeding risk was likely increased in this patient due to several factors including the surgical procedure and concurrent antithrombotic therapy. In conclusion, the risks associated with hypoxemia and increased bleeding must be considered for the safe provision of general anesthesia during palatoplasty procedures in patients with cyanotic heart disease.