This paper examines the determinants of very low birth weight infant (or neonatal) mortality using the Taiwan National Health Insurance Research database from 1997 to 2009. After infants are discharged from hospital, it is not possible to track their mortality, so the Cox proportional hazard model is used to analyze the very low birth weight infant mortality rate. In order to clarify treatment responsibility and to avoid selective referral effects, we use the number of infants treated in the preceding five years to observe the effect of a physician's and hospital's medical experience on the mortality rate of hospitalized minimal birth weight infants. The empirical results show that, given disease control variables, a higher infant weight, higher quality hospitals, increased hospital medical experience, and higher investment in pediatrics can reduce the mortality rate significantly. However, an increased physician's medical experience does not seem to influence significantly the very low birth weight infant mortality rate.