Summary: We propose a functional censored quantile regression model to describe the time-varying relationship between time-to-event outcomes and corresponding functional covariates. The time-varying effect is modeled as an unspecified function that is approximated via B-splines. A generalized approximate cross-validation method is developed to select the number of knots by minimizing the expected loss. We establish asymptotic properties of the method and the knot selection procedure. Furthermore, we conduct extensive simulation studies to evaluate the finite sample performance of our method. Finally, we analyze the functional relationship between ambulatory blood pressure trajectories and clinical outcome in stroke patients. The results reinforce the importance of the morning blood pressure surge phenomenon, whose effect has caught attention but remains controversial in the medical literature.