The linear quantile regression estimator is very popular and widely used. It is also well known that this estimator can be very sensitive to outliers in the explanatory variables. In order to overcome this disadvantage, the usage of the least trimmed quantile regression estimator is proposed to estimate the unknown parameters in a robust way. As a prominent measure of robustness, the breakdown point of this estimator is characterized and its consistency is proved. The performance of this approach in comparison with the classical one is illustrated by an example and simulation studies.