Ventricular dysfunction affects survival in patients with single right ventricle (RV), and remains one of the primary indications for heart transplantation. Since it is challenging to predict the capacity of patients with ventricular dysfunction to proceed to the stage II procedure, we sought to identify factors that would be associated with death or heart transplantation without achieving stage II for single RV patients with ventricular dysfunction after Norwood procedure. The Single Ventricle Reconstruction (SVR) trial public-use database was used. Patients with a RV ejection fraction less than 44% or a RV fractional area of change less than 35% on the post-Norwood echocardiogram were included. Parametric risk hazard analysis was used to identify risk factors for death or transplantation without achieving stage II. Of 365 patients with ventricular function measurements on the post-Norwood echocardiogram, 123 (34%) patients had RV dysfunction. The transplantation-free survival was significantly lower for those with ventricular dysfunction compared to those with normal function (log rank Chi-square = 4.23, p = 0.04). Furthermore, having a Blalock–Taussig (BT) shunt, a large RV, a post-Norwood infectious complication, and a surgeon who performs five or less Norwood per year were independent risk factors for death or transplantation without achieving stage II. The predicted 6-month transplantation-free survival for patients with all four identified risk factors was 1% (70% CI 0–13%). Early heart transplantation referral might be considered for post-Norwood patients with BT shunt and RV dysfunction, especially if other high-risk features are present.