<p>Quantile regression (QR) has become an important tool to measure dependence of response variable’s quantiles on a number of predictors for heterogeneous data, especially heavy-tailed data and outliers. However, it is quite challenging to make statistical inference on distributed high-dimensional QR with missing data due to the distributed nature, sparsity and missingness of data and non-differentiable quantile loss function. To overcome the challenge, this paper develops a communication-efficient method to select variables and estimate parameters by utilizing a smooth function to approximate the non-differentiable quantile loss function and incorporating the idea of the inverse probability weighting and the penalty function. The proposed approach has three merits. First, it is both computationally and communicationally efficient because only the first- and second-order information of the approximate objective function are communicated at each iteration. Second, the proposed estimators possess the oracle property after a limited number of iterations without constraint on the number of machines. Third, the proposed method simultaneously selects variables and estimates parameters within a distributed framework, ensuring robustness to the specified response probability or propensity score function of the missing data mechanism. Simulation studies and a real example are used to illustrate the effectiveness of the proposed methodologies.</p>