We propose a functional censored quantile regression model to study the relationship between the time to stroke recurrence and the dynamic blood pressure levels, where the time-varying effect is an unspecified function. The B-spline method is used to approximate the coefficient function, which operationally reduces the problem to the parametric estimation. A generalized approximate cross-validation method is devel- oped to select the number of knots by minimizing the expected loss. We demonstrate the asymptotic properties of the estimation and knots selection procedure. Further, we conduct extensive simulation to evaluate the finite sample performance of our method and apply it to analyze the blood pressure and clinical outcome in transient ischemic attack or ischemic stroke data. The results reinforce the importance of the morning surge phenomenon, whose effect has caught attention but remains controversial in the medical literature.