This paper addresses the quantile regression task when some non-negligible portion of data are corrupted by accidental factors such as temporary sensor malfunctions. Here, the task is to find the empirical quantile of the "reliable" data with the "unreliable" ones excluded. For this task, we propose the MC-pinball loss which is the composition of the minimax concave (MC) penalty and the pinball loss. The simulation results show that the proposed approach yields reasonable estimates of the true quantile. A potential benefit of the proposed approach is also shown with respect to the parameter tuning.