Addition of the middle hepatic vein (MHV) or reconstruction of its tributaries to increase noncongestive graft volume is expected to improve graft function in right liver living donor liver transplantation (LDLT). However, the relationship between noncongestive graft volume and graft function after transplantation has not been clarified and definitive criteria for the reconstruction of MHV tributaries have yet to be established. We analyzed 29 right liver LDLT cases. The noncongestive graft weight was calculated as the total weight of the graft regions drained by hepatic veins reconstructed without postoperative occlusion. We calculated the noncongestive graft-to-recipient weight ratio (ncGRWR) by comparing it to the GRWR. Indocyanine green (ICG) clearance results on days 1 and 3 were significantly correlated with ncGRWR, but not with GRWR. Patients were then divided into 2 groups based on ncGRWR: lower than the median (L-ncGRWR group) and above the median (H-ncGRWR group). ICG clearance in the H-ncGRWR group was significantly better on days 1 and 3. For a different analysis, the patients were again divided into 2 groups, those with and without prolonged cholestasis after transplantation. ncGRWR was significantly lower in patients with prolonged cholestasis, and 7 of 9 patients with an ncGRWR value lower than 0.65 suffered from prolonged cholestasis. Our results demonstrated that the noncongestive volume of a right liver graft has a significant association with early graft function. Further, ncGRWR can play a key role in preoperative determination for additional vein reconstruction of MHV tributaries. When the estimated ncGRWR value with reconstruction of only the right hepatic vein (RHV) (+ inferior right hepatic vein [IRHV]) is less than 0.65, additional vein reconstruction of MHV tributaries should be planned.