<p>This paper considers simultaneous inference of quantiles for high-dimensional data. Based on a newly derived non-asymptotic Bahadur representation, we develop a systematic distributional theory for sample quantiles. In particular, we show that the distribution of the normalized maximum deviation between sample and population quantiles is close to that of a centered Gaussian random vector with certain covariance structure which is typically unknown in practice. To circumvent the difficult problem of estimating the unknown covariance structure, we propose a weighted bootstrap calibration and introduce a general procedure to construct simultaneous confidence intervals for quantiles in the high-dimensional setting. Our theoretical results justify the validity of the proposed procedure.</p>