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As an emerging learning method belonging to the family of neural networks, the broad learning system (BLS) has been recently proved to be effective and efficient to perform regression tasks in various scenarios. However, if data are contaminated by some outliers or other more complex non-Gaussian noises, the learning performance of BLS may be severely compromised, due to its dependence on the conventional mean square error criterion. To enhance the robustness of BLS to deal with contaminated data, a new similarity measure termed generalized multikernel correntropy (GMKC) is proposed in this paper, and some important properties of this measure are investigated. On the basis of GMKC, a general BLS variant called GMKC-based BLS (GMKC-BLS), is subsequently developed to perform regression tasks with contaminated data. Since GMKC with its unique design actually builds a unified framework for many robust and popular metrics, GMKC-BLS is expected to be with excellent robustness and adaptability, and provides a competitive solution to the regression problems with contaminated data. Meanwhile, GMKC could be integrated with other neural network-based methods to further enhance their robustness. Experimental results on different regression datasets demonstrate the performance superiority of GMKC-BLS compared to the standard BLS and its robust variants. [ABSTRACT FROM AUTHOR]