We propose a class of landmark cure rate models by incorporating time-dependent covariates. The landmark approach enables us to obtain dynamic predictions of a patient's survival probabilities as new clinical information emerges during the follow-up time. The proposed method extends the landmark model for failure time data with a possible cure fraction. We specify a series of landmark time points, and for each of time point, we construct a landmark data set consisting of only those at-risk individuals at the landmark time. The time-dependent covariates can be fixed at the values evaluated at the landmark time point. Through landmarking, our framework accommodates the Cox proportional hazards model, accelerated failure time model and censored quantile regression model in the presence of a cure proportion. We conduct simulation studies to assess the estimation accuracy of the proposed method, and illustrate it with data from a heart transplant study.