The modern problems of optimization, estimation, signal processing, and image recognition deal with data of huge dimensions. It is important to develop effective methods and algorithms for such problems. An important idea is the construction of low-dimension approximations to large-scale data. One of the most popular methods for this purpose is the principal component analysis (PCA), which is, however, sensitive to outliers. There exist numerous robust versions of PCA, relying on sparsity ideas and l1 techniques. The present paper offers another approach to robust PCA exploiting Huber's functions and numerical implementation based on the Iterative Reweighted Least Squares (IRLS) method.