Robust estimation of multiple-structured data is a fundamental problem in computer vision. Based on the linear EIV model, a novel robust growing algorithm is proposed to estimate the inherent model parameters from the contaminated data. The algorithm starts from an initial subset in the area of structured data. Then it adds the model data points to the subset and updates the parameter estimate iteratively. At each iteration, the C-Step method originated from the MCD estimator is adopted to adjust the subset and to ensure the robustness of the algorithm by ejecting outliers. Based on the structured density assumption that the gross errors should be no denser than the structured data, otherwise the structured data would be indistinguishable from the gross errors; the mean shift algorithm is adopted to ensure a good initialization for the robust growing algorithm. Experiments show that the proposed algorithm can deal with contaminated data, which contain multiple structures and high percentage of gross errors efficiently, and has higher robustness and accuracy than the existing robust estimation algorithms.