The panel-data regression models are frequently applied to micro-level data, which often suffer from data contamination, erroneous observations, or unobserved heterogeneity. Despite the adverse effects of outliers on classical estimation methods, there are only a few robust estimation methods available for fixed-effects panel data. A new estimation approach based on two different data transformations is therefore proposed. Considering several robust estimation methods applied to the transformed data, the robust and asymptotic properties of the proposed estimators are derived, including their breakdown points and asymptotic distributions. The finite-sample performance of the existing and proposed methods is compared by means of Monte Carlo simulations.