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Network component analysis (NCA) is an efficient method of reconstructing the transcription factor activity (TFA), which makes use of the gene expression data and prior information available about transcription factor (TF) - gene regulations. We propose ROBust Network Component Analysis (ROBNCA), a novel iterative algorithm that explicitly models the possible outliers in the microarray data. ROBNCA algorithm provides a closed form solution for estimating the connectivity matrix, which was not available in prior contributions. The ROBNCA algorithm is compared to FastNCA and the Non-iterative NCA (NI-NCA) and is shown to estimate the TF activity profiles as well as the TF-gene control strength matrix with a much higher degree of accuracy than FastNCA and NI-NCA, irrespective of varying noise, and/or amount of outliers in case of synthetic data. The run time of the ROBNCA algorithm is comparable to that of FastNCA, and is hundreds of times faster than NI-NCA.