We establish the asymptotic theory of least absolute deviation estimators for AR(1) processes with autoregressive parameter satisfying $n(ρ_n-1)\toγ$ for some fixed $γ$ as $n\to\infty$, which is parallel to the results of ordinary least squares estimators developed by Andrews and Guggenberger (2008) in the case $γ=0$ or Chan and Wei (1987) and Phillips (1987) in the case $γ\ne 0$. Simulation experiments are conducted to confirm the theoretical results and to demonstrate the robustness of the least absolute deviation estimation.