<p>Composite quantile regression (CQR) provides a robust and statistically efficient alternative to mean regression by aggregating information across multiple quantile levels. This paper develops two communication-efficient distributed estimators for CQR tailored to distributed systems where data are non-randomly distributed across machines and the CQR loss is non-smooth. We first introduce a convolution smoothing scheme that renders the composite quantile loss differentiable, and within this smoothed CQR (SCQR) framework construct a Poisson subsampling estimator. Theoretically, we establish the subsampling estimator’s rates of convergence and asymptotic normality, and we derive L-optimal sampling probabilities, thereby establishing the estimator’s validity. Building on this, we propose a distributed SCQR estimator with Poisson subsampling (DSCQR-P) that transmits only a small Poisson subsample and gradient summaries from workers to the master, achieving strong communication savings and practical feasibility. With Newton–Raphson updates, Hessians computed from the aggregated subsample are more stable than those from any single shard, and we prove that DSCQR-P is asymptotically equivalent to the global full-sample estimator. For high-dimensional settings, we further develop a regularized distributed SCQR (DSCQRH-P) with an efficient Local Adaptive Majorize-Minimization implementation and show its oracle property. Extensive simulations and two real data applications demonstrate that our methods deliver scalability, robustness, and statistical efficiency while substantially reducing computational and communication costs.</p>