Let F(t|x) be the distribution function of the life time of a unit with covariate x in the Cox proportional hazard model. Let ξ(p, x) be the pth quantile of F(·|x). We consider the problem of constructing confidence bands/regions for ξ (·,·). We develop the asymptotic theory for the proposed bands. The results of Monte Carlo simulation studies to compare the bands with the other competing bands are presented. As illustrated, we apply the proposed bands to the Stanford Heart Transplant Data.