Forest height is an essential input parameter for forest biomass estimation, ecological modeling, and the carbon cycle. Tomographic synthetic aperture radar (TomoSAR), as a three-dimensional imaging technique, has already been successfully used in forest areas to retrieve the forest height. The nonparametric iterative adaptive approach (IAA) has been recently introduced in TomoSAR, achieving a good compromise between high resolution and computing efficiency. However, the performance of the IAA algorithm is significantly degraded in the case of a small tomographic aperture. To overcome this shortcoming, this paper proposes the robust IAA (RIAA) algorithm for SAR tomography. The proposed approach follows the framework of the IAA algorithm, but also considers the noise term in the covariance matrix estimation. By doing so, the condition number of the covariance matrix can be prevented from being too large, improving the robustness of the forest height estimation with the IAA algorithm. A set of simulated experiments was carried out, and the results validated the superiority of the RIAA estimator in the case of a small tomographic aperture. Moreover, a number of fully polarimetric L-band airborne tomographic SAR images acquired from the ESA BioSAR 2008 campaign over the Krycklan Catchment, Northern Sweden, were collected for test purposes. The results showed that the RIAA algorithm performed better in reconstructing the vertical structure of the forest than the IAA algorithm in areas with a small tomographic aperture. Finally, the forest height was estimated by both the RIAA and IAA TomoSAR methods, and the estimation accuracy of the RIAA algorithm was 2.01 m, which is more accurate than the IAA algorithm with 3.25 m.