Cox proportional hazards (PH) is known as the most popular model for the analysis of multivariate survival data. The main assumption of the model is that the hazard ratio among any two individuals in the population is constant over time. The violation of this assumption, however, may cause serious issues such as overestimation or underestimation of hazard risks and reducing the power of related statistical tests. The main objective of this research, therefore, is to extend the Cox PH model by adding time-dependent variables into the model to cope with the presence of non-PH. The proposed model, moreover, is applied to under-five mortality data based on Indonesian Demographic and Health Survey (IDHS) 2012. The results showed that the Akaike’s Information Criterion (AIC) and Bayesian Information Criterion (BIC) values of the extended Cox model with time-dependent variables are much lower than the Cox PH model. This means that the extended Cox model can increase significantly the goodness-of-fit of the Cox PH model to under-five mortality data in Indonesia.