Let ξ$_{p}$(z$_{0}$) be the pth quantile of the distribution of the survival time of an individual with time-invariant covariate vector z$_{0}$ in the additive risk model. We propose an estimator of (ξ$_{p}$(z$_{0}$) and derive its asymptotic distribution, and then construct an approximate confidence interval of ξ$_{p}$(z$_{0}$) . Simulation studies are carried out to investigate performance of the proposed estimator far practical sample sizes in terms of empirical coverage probabilities. Also, the estimator is illustrated on small cell lung cancer data taken from Ying, Jung, and Wei (1995) .d Wei (1995) .