Analysis of real-life high-dimensional data is often challenged by the complexity of measurement errors on the covariates or missing data. Several different methods have recently been developed to tackle this challenge. Despite important progresses, these approaches often require additional computational efforts comparing with those standard approaches in the settings where the complexity of error-in-variables is absent. Motivated by these recent works, we propose a new direct, computationally simple approach, which enjoys the same computational convenience of standard Dantzig estimator in the non-contamination case and requires no additional tuning parameter. The new estimator can be easily implemented using any existing software for linear programming. Theoretically, we derive the estimation error bound, which achieves the near-optimal minimax rate for additive measurement error model. Simulation studies demonstrate that the proposed estimator has similar performance while requiring substantially less computational cost comparing with those recent competitors.