Parents’ time on child care has profound impact on children’s human capital formation. Previous studies on parental time with children, which use ordinary least squares and Tobit model as their estimation method, focus on conditional mean of parental time with children. As far as we know, no empirical attention has been paid to parents that spent little time with children. Since wage is likely to be endogenous to time spent with children, this thesis uses censored quantile instrumental variable estimator to analyze the determinants of time spent on child care. Based on micro data from the 2003-2010 American Time Use Survey, we found that the dummy variable for non-hispanic non-black and non-white is statistically significantly negatively associated with time spent with children. This result implies that more resources should be directed to facilitating and promoting parental time with children among non-hispanic non-black and non-white parents.