When analyzing time-to-event data in clinical and epidemiological studies with missing covariate values, the missing at random assumption is commonly adopted. It assumes that missingness depends on the observed data, including the observed outcome which is the minimum of survival and censoring time. However, in certain settings, the missingness is likely related to the survival time but not to the censoring time. This occurs for example when covariates are measured at baseline and censoring is administrative. In this case, the covariate missingness mechanism is nonignorable as the survival time is censored, and it creates challenge in data analysis. We propose two different estimators to deal with such survival-time-dependent covariate missingness based on the well known Cox regression models. Our method is based on inverse propensity weighting with the propensity estimated by nonparametric kernel regression.