This paper studies distributed estimation and support recovery for high-dimensional linear regression model with heavy-tailed noise. To deal with heavy-tailed noise whose variance can be infinite, we adopt the quantile regression loss function instead of the commonly used squared loss. However, the non-smooth quantile loss poses new challenges to high-dimensional distributed estimation in both computation and theoretical development. To address the challenge, we transform the response variable and establish a new connection between quantile regression and ordinary linear regression. Then, we provide a distributed estimator that is both computationally and communicationally efficient, where only the gradient information is communicated at each iteration. Theoretically, we show that the proposed estimator achieves the optimal convergence rate (i.e., the oracle convergence rate when all the data is pooled on a single machine) without any restriction on the number of machines. Moreover, we establish the theoretical guarantee for the support recovery. The simulation and real data analysis are provided to demonstrate the effectiveness of our estimator.